Answers
2. When the bottle is pushed downwards the ketchup moves with the bottle. When the bottle is stopped by our hand, the inertia of the ketchup keeps it going and out if the bottle.
3. Before the rest-end collision the body (and head) move with the sand velocity. At the moment of impact the body of a person accelerates forward but the head of the person tried to remain with its initial velocity (because of its inertia) and that means the head appears to move abruptly backwards.
4. While skating, both you and the skateboard move with the same velocity. If the skateboard stops suddenly the person’s inertia would make it continue to move forward with its original velocity.
5. When passenger in a car and the car swerves suddenly to the left, your inertia will want to maintain your velocity. You end up hitting the side of the car as it comes towards you.
Related Questions
It takes more time to find a value in a hash table data structure than to find a value in a doubly linked list data structure. True or False
Answers
False.In a hash table data structure, the time complexity for finding a value (retrieving an element) is typically O(1) on average, assuming a good hash function and a well-distributed set of keys. This means that the time it takes to find a value is constant, regardless of the size of the data structure.
On the other hand, in a doubly linked list data structure, finding a value requires traversing the list from the beginning or end until the desired value is found. The time complexity for finding a value in a doubly linked list is O(n), where n is the number of elements in the list. This means that the time it takes to find a value in a doubly linked list increases linearly with the size of the list.Therefore, it takes more time to find a value in a doubly linked list data structure compared to a hash table data structure.
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what is the initial velocity of the baseball? use: positive x (east), positive y (north), positive z (up)
Answers
More information is needed to provide a specific answer. Please provide additional context or data related to the initial velocity of the baseball.
To find the initial velocity of the baseball, we can use the kinematic equations of motion. Since the baseball is thrown at an angle, we need to break down the initial velocity into its x, y, and z components. We know that the initial height of the baseball is 1.8 meters, and the time it takes to reach its maximum height is 1.0 seconds. From this, we can calculate the vertical component of the initial velocity using the equation vf = vi + gt, where vf = 0 m/s, vi is the initial velocity, g is the acceleration due to gravity \((-9.8 m/s^2\)), and t is the time.
Solving for vi, we get vi = 9.8 m/s.
To find the horizontal component of the initial velocity, we can use the equation\(x = vit + 1/2at^2\), where x is the distance travelled in the x-direction (which is 18 meters), vi is the initial velocity in the x-direction, a is the acceleration in the x-direction (which is 0 m/s^2 since there is no horizontal force acting on the ball), and t is the time of flight (which we can calculate using the time it takes for the ball to reach its maximum height). Solving for vi, we get vi = x/t = 18/2.0 = 9.0 m/s. So the initial velocity of the baseball can be expressed as <9.0, 9.8, 0> m/s, where the x-component is 9.0 m/s (to the right), the y-component is 9.8 m/s (upward), and the z-component is 0 m/s (since there is no initial velocity in the z-direction).
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What happens when heavy exercise results in too much acid in the human body? Excess H+ is absorbed by bicarbonate ions.
Bicarbonate releases one H+ to become carbonate.
H2CO3 is formed from H2O and CO2.
Bicarbonate is formed from carbonate.
Answers
Answer:
A: Excess H+ is absorbed by bicarbonate ions.
Explanation:
When forces of 5 N and 7 N respectively act on an object. When will the resultant of the two vectors be at a maxium
Answers
Answer:
F = 12 N
Explanation:
Given that,
Force of 5 N and 7 N respectively act on an object.
We need to find the resultant of the two vectors be at a maximum.
Force will be maximum when two forces acts in same direction. It means we can simply add them i.e.
F = 5 N + 7 N
F = 12 N
Hence, the resultant force is 12N.
What are the three components of the cell theory
Answers
2. cells are the basic units of structure and function for living things
3. all cells come from pre-existing cells. (organisms grow by adding on more cells, not by increasing the sizes of the cell)
Answer:
The first component of the cell theory says that all living things are made of cells. The second component of the cell theory states that cells are the basic structure and function of living things. The last component of the cell theory says that cells come from other cells.
Explanation:
Srry this took so long but hope this helps this is also the right answer have a good day
(P.S please mark the helpfull )
Which one of the following statements is true concerning the work done by an external force in moving an electron at constant speed between two points in an electrostatic field?
A) The work done is always zero joules.
B) The work done is always positive.
C) The work done only depends on the speed of the electron.
D) The work done depends on the total distance covered.
E) The work done depends only on the displacement of the electron
Answers
The true statement concerning the work done by an external force in moving an electron at constant speed between two points in an electrostatic field is E) The work done depends only on the displacement of the electron.
To explain this, consider the following steps:
1. The work done by an external force is given by the equation W = F × d × cosθ, where W is the work done, F is the force applied, d is the displacement, and θ is the angle between the force and displacement vectors.
2. When moving an electron at constant speed in an electrostatic field, the external force should be equal in magnitude but opposite in direction to the electrostatic force acting on the electron.
3. This means that the angle θ between the force and displacement vectors will be 0 degrees, and cosθ = 1.
4. Therefore, the work done (W) depends only on the product of the force applied (F) and the displacement (d).
So, the correct answer is E) The work done depends only on the displacement of the electron.
A bus travelling at 30m/s along a straight road passes throu a stationary taxi cab.the can begins to move 5seconds later within a uniform acceleration of 2metres per seconds square in the same direction as the bus.1.calculate the time taken by the cab to meet the bus.2.distance the cab has travelled to catch-up with the bus
Answers
(1) The time taken by the cab to meet the bus is 18.96 seconds.
(2) The distance the cab has travelled to catch-up with the bus is 718.96 m.
Distance between the bus and the cab
The distance between the bus and the cab when the cab begins to move is calculated as follows;
D = speed x time
D = 30 m/s x 5 s
D = 150 m
Velocity of the cabThe velocity of the cab when it begins to move is calculated as follows;
v = at
(v - 30)t = D
(at - 30)t = 150
(2t - 30)t = 150
2t² - 30t = 150
2t² - 30t - 150 = 0
solve the quadratic equation using formula method
t = 18.96 seconds
Distance traveled by the cabD = vt
D = 2t²
D = 2(18.96²)
D = 718.96 m
Thus, the time taken by the cab to meet the bus is 18.96 seconds. The distance the cab has travelled to catch-up with the bus is 718.96 m.
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if the magnetic field steadily decreases from b to zero during a time interval t , what is the magnitude i of the induced current? express your answer in terms of x , y , b , t , and the resistance r of the wire.
Answers
The magnitude of the induced current can be calculated using Ohm's law:
i = ε/r = B*A/(r*t) = b*(xy)/(rt)
Thus, the magnitude i of the induced current can be expressed in terms of x, y, b, t, and the resistance r of the wire as
i = (xy * b) / (t * r) , where
- b is the initial magnitude of the magnetic field,
- t is the time interval during which the magnetic field decreases to zero,
- r is the resistance of the wire,
- x is the length of the wire exposed to the magnetic field, and
- y is the length of the wire not exposed to the magnetic field.
The magnitude i of the induced current can be found using Faraday's Law of Electromagnetic Induction. Faraday's Law states that the induced electromotive force (EMF) is equal to the negative rate of change of the magnetic flux through a closed loop.
1. First, calculate the change in magnetic field (ΔB) which is given by:
ΔB = 0-b = -b.
2. Next, calculate the change in magnetic flux (ΔΦ) through the closed loop. Since we are given that the loop has dimensions x and y, the area A of the loop is A = xy. The change in magnetic flux is given by:
ΔΦ = A * ΔB = xy *(-b).
3. Now, calculate the rate of change of magnetic flux (dΦ/dt) over the given time interval t:
dΦ/dt = ΔΦ / t = -(xy * b) / t.
4. According to Faraday's Law, the induced EMF (ε) is equal to the negative rate of change of magnetic flux:
ε = -dΦ/dt.
= -(-xy*b) / t
= xy*b / t.
5. Finally, use Ohm's Law to find the magnitude i of the induced current, which is given by:
i = ε / r, where r is the resistance of the wire.
Putting it all together, we get,
i = (xy * b) / (t * r).
So, the magnitude i of the induced current is expressed as
i = (xy * b) / (t * r)
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12. Which of the following statements is accurate?
A. If an object's velocity is changing, it's experiencing either acceleration or deceleration.
B. If an object's velocity decreases, then the object is accelerating
C. If an objects said to be decelerating, its velocity must be increasing,
D. If an object's velocity remains constant, its acceleration must be increasing.
Answers
Answer:
Option (a) is correct
Explanation:
The acceleration of an object is defined as the rate of change of velocity. Mathematically, it can be written as :
\(a=\dfrac{v-u}{t}\)
Where
v and u are final and initial velocity
It is clear that if there is some change in velocity, it means the object is experiencing either acceleration or deceleration. Hence, the correct option is (a).
Answer:
a
Explanation:
Help me as pleasessss help with 1,2 and 3
Answers
2.) Physical Properties
3.) Flammability, Reactivity, Ability to Rust
are fossil fuels a renewable energy source because they are formed from living things
Answers
Answer:
Fossil fuels are non-renewable . They took a very long time to form and we are using them up faster than they can be replaced - once they have all been used up, they cannot be replaced.
What is the mass of an object that is accelerating at a rate of 25 m/s² and is using 15 N of force?
Answers
Given F = 15 N
A = 25 m/s^2
15 N = M * 25m/s^2
M = 15/25 = 3/5
3/5 * 2/2 = 6/10 = 0.6
Solution: 0.60 Kg
what are duplet and octet elements??
Answers
The marker posts on a highway are 0.1 miles apart. If a truck is timed taking 5
seconds between posts, how fast is the truck going (in MPH; there are 3600 seconds
in an hour)?
Answers
Answer:
v= 72 miles/hour
Explanation:
Speed
The speed is the ratio of the distance x traveled by an object and the time t it took to complete the distance.
We calculate the speed as follows:
\(\displaystyle v=\frac{x}{t}\)
The truck was timed taking t=5 seconds between posts that are x=0.1 miles apart.
The speed of the truck is:
\(\displaystyle v=\frac{0.1}{5}\)
\(v=0.02\ miles/sec\)
Since 1 hour = 3,600 seconds:
v=0.02 * 3,600 miles/hour
v= 72 miles/hour
A ball of mass 0.12kg is hit by a tennis player. The velocity of the ball changes from 0m/ s to 5.0m/s in 0.60s. What is the average resultant force acting on the ball while it is being hit?
A 1.0N B 2.5N C 3.6N D 8.3N
(Please add explanation)
Answers
Answer:
A. 1.0NExplanation:
According to Newton's second law
F = ma
m is the mass = 0.12kg
a is the acceleration = v-u/t
a = 5-0/0.6
a = 5/0.6
a = 8.333m/s²
Get the force
F = 0.12 * 8.333
F = 1.0N
Hence the average resultant force acting on the ball while it is being hit is 1.0N
What pressure would the butane gas sample have at 120.0 mL?
Answers
The pressure of the butane gas sample at 120.0 mL can be determined by using the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
To find the pressure of the butane gas sample at 120.0 mL, we need additional information such as the number of moles and the temperature of the gas. Once we have these values, we can use the ideal gas law equation, PV = nRT, to calculate the pressure.
1. Determine the values: Gather the known values for the problem, such as the volume (V = 120.0 mL) and any other given information, such as the number of moles (n) and the temperature (T).
2. Convert the volume: If necessary, convert the volume to the appropriate unit for the ideal gas law equation. The ideal gas law typically requires volume to be in liters, so if the given volume is in milliliters, divide it by 1000 to convert to liters.
3. Plug in the values: Substitute the known values into the ideal gas law equation, PV = nRT. Make sure to use consistent units for all the variables.
4. Solve for pressure: Rearrange the equation to solve for pressure (P). Divide both sides of the equation by the volume (V) to isolate pressure: P = (nRT) / V.
5. Calculate the pressure: Substitute the known values into the equation and perform the necessary calculations to find the pressure of the butane gas sample at 120.0 mL.
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1. -------- of an object is the change in velocity per unit time.
a) Displacement b) Acceleration c) Average velocity d) Angular velocity.
2. The motion of freely falling body is an example of ----- motion.
a) Uniform motion b) Non -uniform motion c) Uniformly accelerated motion. d) None of these.
Answers
Answer:
A
Explanation:
acceleration is defined as the rate of change of velocity with time
Rosa pours a cup of boiling water into a pot of room temperature water. According to the second law of
thermodynamics, what will occur?
O Thermal energy from the room temperature water will continuously flow to the boiling water.
O Thermal energy from the room temperature water will flow to the boiling water until all of the water in the pot is at
a single temperature.
Thermal energy from the boiling water will continuously flow to the room temperature water.
Thermal energy from the boiling water will flow to the room temperature water until all of the water in the pot is at
a single temperature.
Answers
Answer: D. Thermal energy from the boiling water will flow to the room-temperature water until all of the water in the pot is at a single temperature.
Explanation:
This is because thermal energy moves from warmer objects to cooler objects, until they are at the same level of thermal energy or temperature.
Answer:
Answer is D
Explanation:
Edge 2020
a heart pacemaker fires 89 times a minute, each time a 36.0-nf capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. what is the value of the resistance?
Answers
Answer:
The value of the resistance is 3.99 kΩ
Explanation:
The value of the resistance, given that a heart pacemaker fires 89 times a minute, and each time a 36.0-nf capacitor is charged to 0.632 of its full voltage, is 3.99 kΩ.
How to determine the value of the resistance?
We know that a pacemaker fires 89 times per minute, charging a 36.0-nf capacitor each time, and the capacitor is charged to 0.632 of its full voltage.
The formula for determining the time constant is: τ = RC and the formula for determining the voltage of a capacitor as it charges is: Vc = Vmax(1 - e^(-t/τ)) Using the following information, we can compute the value of the time constant:
τ = RCτ = (0.632Vmax * C) / IV max = 9 V The value of the time constant is τ = RC = (0.632Vmax * C) / I = (0.632 * 9 * 10^-3) / I = 5.67 * 10^-3 / I To find the value of the resistance, R, we'll use the frequency of the pacemaker (f = 89/60 Hz), which is the number of times it fires per second.
RC = 1/fRC = (5.67 × 10^-3)/IR = RCfR = [(5.67 × 10^-3)/I](89/60)R = 3.99 kΩ
Therefore, the value of the resistance, given that a heart pacemaker fires 89 times a minute, and each time a 36.0-nf capacitor is charged to 0.632 of its full voltage, is 3.99 kΩ.
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Una partícula se mueve en el plano XY efectúa un desplazamiento mientras actúa sobre ella una fuerza constante. X= (4i + 3j) m, F = (16i + 12j) N a) Calcule la magnitud del desplazamiento y la de la fuerza. B) Calcule el trabajo realizado por la fuerza F c) Calcule el ángulo entre F y x.
Answers
Answer:
a) La magnitud del desplazamiento es de 5 m
La magnitud de la fuerza es 20 N
b) El trabajo realizado por la fuerza es de 100 J
c) El ángulo entre la fuerza y el plano es 0 °
Explanation:
a) La magnitud del desplazamiento se encuentra por la relación;
\(\left | X \right | = \sqrt{X_{x}^{2}+X_{y}^{2}}\)
Lo que da;
\(\left | X \right | = \sqrt{4^{2}+3^{2}} = 5 \ m\)
De manera similar, la magnitud de la fuerza, F, se encuentra como sigue;
\(\left | F \right | = \sqrt{F_{x}^{2}+F_{y}^{2}}\)
Lo que da;
\(\left | F \right | = \sqrt{16^{2}+12^{2}} = 20 \ N\)
b) El trabajo, W, realizado por la fuerza = Fuerza, F × Distancia, X
∴ Ancho = 20 N × 5 m = 100 N · m = 100 J
c) La dirección de la fuerza viene dada por la siguiente fórmula;
\(tan^{-1} \left (\dfrac{F_y}{F_x} \right ) = tan^{-1} \left (\dfrac{12}{16} \right ) = 38.9^{\circ}\)
La dirección del plano viene dada por la siguiente fórmula;
\(tan^{-1} \left (\dfrac{X_y}{X_x} \right ) = tan^{-1} \left (\dfrac{3}{4} \right ) = 38.9^{\circ}\)
Por tanto, el ángulo entre la fuerza y el plano = 0 °
La fuerza actúa a lo largo del plano.
Given the graph below, the resistance of the wire in Ohms is:
a 0.25
b 4
c 3.75
d 0
Answers
Answer:
C . 3.75 Ohms
Explanation:
V = IR
R = V / I
From the graph, you pick a value for potential difference and find its corresponding current.
The resistance of the wire in Ohms is 3.75 Ω, therefore the correct answer is option C
What is resistance?Resistance is the obstruction of electrons in an electrically conducting material.
The mathematical relation for resistance can be understood with the help of the empirical relation provided by Ohm's law.
V=IR
where V is the voltage
I is the current
From the voltage-current graph, one can know the resistance by calculating the slope of the graph
As shown in the graph the variation of the voltage with the current
Y axis represents the voltage and the X axis represents the current
slope = variation in the Y coordinate /variation in the X coordinate
resistance = variation in the voltage /variation in the current
= (30 - 0 )/ (8-0 )
= 3.75 Ω
Thus, by observation and calculation from the graph, the resistance of the wire comes out to be 3.75 Ω
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A force of 52 N is applied on the outside of a sphere with a moment of inertia of 12.8 kg-m² and a radius of 0.4 m.
How long will it take to accelerate the sphere from 1.5 rad/s to 8.5 rad/s?
Answers
It will take 4.30 seconds to accelerate the sphere from 1.5 rad/s to 8.5 rad/s.
What is moment of inertia?Moment of inertia, a quantitative measure of the rotational inertia of a body in physics - The resistance that a body exhibits to changing its rotational speed about its axis by the application of a torque (torque). Axis can be internal or external and can be fixed or unfixed.
For the calculation of torque:
τ = F × r × sinθ
τ = Torque
F = force applied (52 N)
r = radius (0.4 m)
θ = angle between force and radius (90°)
τ = 52 × 0.4 × sin90
τ = 52 × 0.4 × 1
τ = 20.8 Nm
Now, for angular acceleration:
τ = α × I
α = τ/I
α = Angular acceleration
τ = Torque (20.8 Nm)
I = moment of inertia (12.8 kg-m²)
α = 20.8/12.8
α = 1.625 rad/s²
Time required by the sphere to accelerate:
α = (ω₂ -ω₁)/t
t = (ω₂ -ω₁)/α
t = (8.5 - 1.5)/1.625
t = 4.30 s
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Consider the polynomial
() = −0. 14 − 0. 153 − 0. 52 − 0. 25 + 1. 2
The true value of its derivative at x=0. 5 is ′
(0. 5) = −0. 9125. Use backward, forward, and centered
first finite differences to estimate the derivative numerically if the step size ∆ = 0. 25, and determine
the percent error between the true value and each of the estimated values (percent error is given by
= −
converted to a percentage. ) What value of ∆ would you have to use for the backward and forward
finite differences to get the same percent error as the centered finite difference (hint: it should be less
than 0. 25. )
Answers
The backward finite difference method for estimating the derivative at x=0.5 is:
(f(0.5) - f(0.25)) / (0.5 - 0.25) = (-0.14 - (-0.4025)) / (0.5 - 0.25) = 0.2625 / 0.25 = 10.5
The percent error between this estimate and the true value is:
|(10.5 - (-0.9125)) / (-0.9125)| * 100% = |11.4125 / (-0.9125)| * 100% = 12.48%
The forward finite difference method for estimating the derivative at x=0.5 is:
(f(0.75) - f(0.5)) / (0.75 - 0.5) = (-0.6275 - (-0.14)) / (0.75 - 0.5) = -0.4875 / 0.25 = -1.95
The percent error between this estimate and the true value is:
|(-1.95 - (-0.9125)) / (-0.9125)| * 100% = |-1.0375 / (-0.9125)| * 100% = 1.14%
The centred finite difference method for estimating the derivative at x=0.5 is:
(f(0.75) - f(0.25)) / (0.75 - 0.25) = (-0.6275 - (-0.4025)) / (0.75 - 0.25) = -0.225 / 0.5 = -0.45
The percent error between this estimate and the true value is:
|(-0.45 - (-0.9125)) / (-0.9125)| * 100% = |0.4625 / (-0.9125)| * 100% = 0.51%
To get the same percent error as the centred finite difference, we would have to use a step size of ∆ = 0.125.
This is because a smaller step size means a smaller difference between the estimates and the true value, and therefore a smaller percent error.
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Please ASAP!!!! For q7 and q8
Answers
Answer:
7.37 degree
8.54
Explanation:
yan po ang sagot sana makatulong
A soccer player kicks a ball with initial velocity of 10m/s at an angle of 30 degrees above the horizontal.....what is the magnitude of the vector
Answers
Answer: 10m/s^2
Explanation:
Given the following :
Initial Velocity(U) = 10m/s
Angle of inclination = 30°
In other to calculate the magnitude of the vector,
We need to resolve into verti AL and horizontal component.
Vertical component of a vector(Uy) = U × Sinθ
Horizontal component(Ux) = U × Cosθ
Uy = 10 × sin30 = 10 × 0.5 = 5m/s
Ux = 10 × Cos30 = 10 × 0.866 = 8.66m/s
Therefore the magnitude equals :
U = √(Uy)^2 + (Ux)^2
U = √5^2 + 8.66^2
U = √25 + 74.9956
U = √99.9956
U = 9.9997799
U = 10m/s^2
Which graph represents a car with positive acceleration?.
Answers
Explanation: a graph showing a steeper or none uniform or increase
light from a certain laser has an intensity of 402 mw/m2. what will be its radiation pressure if it is absorbed? answer in pa, with at least 3 significant figures.
Answers
The radiation pressure of the laser would be 1.34 x 10⁻⁶ Pa if it is absorbed.
The radiation pressure can be calculated using the formula P = I/c, where P is the radiation pressure, I is the intensity of the laser, and c is the speed of light.
Using the given intensity of 402 mw/m2, we convert it to SI units by multiplying by 10⁶ to get 402 W/m2.
Thus, the radiation pressure would be P = (402 W/m2) / (3.00 x 10⁸ m/s) = 1.34 x 10⁻⁶Pa.
Therefore, the radiation pressure of the laser would be 1.34 x 10⁻⁶ Pa if it is absorbed.
The concept of radiation pressure is based on the fact that light, despite being massless, carries momentum. When light is absorbed or reflected by an object, it exerts a pressure on that object. This pressure is proportional to the intensity of the light and the surface area of the object.
In this case, we are given the intensity of the laser as 402 mw/m2. However, it is important to note that this intensity is in milliwatts and needs to be converted to watts to be used in the formula. Thus, we convert the intensity to SI units by multiplying it by 10⁶ to get 402 W/m2.
Using the formula P = I/c, where P is the radiation pressure, I is the intensity of the laser, and c is the speed of light, we can calculate the radiation pressure. Substituting the values, we get P = (402 W/m2) / (3.00 x 10⁸ m/s) = 1.34 x 10⁻⁶Pa.
Therefore, the radiation pressure of the laser would be 1.34 x 10⁻⁶ Pa if it is absorbed.
The radiation pressure of a laser can be calculated using the formula P = I/c, where P is the radiation pressure, I is the intensity of the laser, and c is the speed of light. In this case, the given intensity of 402 mw/m2 needs to be converted to SI units by multiplying it by 10⁶ to get 402 W/m2. Substituting the values in the formula, we get the radiation pressure as 1.34 x 10⁻⁶ Pa.
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earth moves in an elliptical orbit with the sun at one of the foci. the length of half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. find the minimum distance (perihelion) and the maximum distance (aphelion) of earth from the sun. perihelion km aphelion km
Answers
The perihelion distance (minimum distance) is approximately 147,096,417.4 kilometers, and the aphelion distance (maximum distance) is approximately 152,099,545.4 kilometers.
To find the perihelion and aphelion distances of Earth's orbit, we can use the properties of an ellipse. The perihelion is the point in the orbit where Earth is closest to the Sun, and the aphelion is the point where Earth is farthest from the Sun.
Given:
Length of half of the major axis (a) = 149,598,000 kilometers
Eccentricity (e) = 0.0167
The formula to calculate the perihelion (r₁) and aphelion (r₂) distances is:
r₁ = a(1 - e)
r₂ = a(1 + e)
Substituting the given values into the formulas, we get:
r₁ = 149,598,000 km * (1 - 0.0167)
= 149,598,000 km * 0.9833
= 147,096,417.4 km
r₂ = 149,598,000 km * (1 + 0.0167)
= 149,598,000 km * 1.0167
= 152,099,545.4 km
Therefore, the perihelion distance (minimum distance) is approximately 147,096,417.4 kilometers, and the aphelion distance (maximum distance) is approximately 152,099,545.4 kilometers.
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)An object with mass m moves along the x-axis. It is observed to have a velocity in the plus x direction with magnitude c
1
t
2
where c
1
is a positive, known constant and t is the time in seconds. At t=1 sec it is observed to be at the point x=D. When does the object reach the point x=2D?
Answers
An object with mass m moves along the x-axis. It is observed to have a velocity in the plus x direction with magnitude c1t2 where c1 is a positive, known constant and t is the time in seconds.
At t=1 sec it is observed to be at the point x=D. When does the object reach the point x=2D?Solution:To solve the given problem, we have to find the time at which the object reaches at the point x=2D.Given velocity of the object, v(t) = c1t^2To calculate the displacement D of an object, we can use the formula for average velocity:
Average velocity v = Displacement / time periodor, Displacement D = average velocity v × time period t
Since the object is at point x=D at time t=1 sec, the displacement of the object will be D.Given velocity of the object, v(t) = c1t^2If t is the time taken by the object to move from point x=D to x=2D, then the displacement of the object will be 2D−D = D.Hence, we have to find the time t at which the displacement D is equal to D.Displacement
D = v × t
Since the velocity of the object is changing with time, we cannot use the formula of displacement as we have used above for calculating D.Therefore, we will use the formula of the displacement when the velocity is changing with time:Displacement D = ∫v(t) dt From the given velocity,
v(t) = c1t^2, we have to integrate this to get the displacement:Displacement D = ∫v(t) dt Integrating with respect to t, we get,
D = c1 (t^3) / 3 + C ... (1)Where C is the constant of integration.To evaluate the constant C, we need additional information.The object has a velocity of c1 at t=0, so we can use this information to evaluate C:At t=0, v(t) = c1×(0)^2 = 0Therefore, C = DUsing the value of C in equation (1), we get,D = c1 (t^3) / 3 + DFor D = 2D, we get,2D = c1 (t^3) / 3 + D2D − D = c1 (t^3) / 3D = c1 (t^3) / 3t^3 = 3D / c1t = (3D / c1) ^ (1/3)Therefore, the object reaches the point x=2D at time t = (3D / c1) ^ (1/3).
Hence, the required time is (3D / c1) ^ (1/3).Ans: (3D / c1) ^ (1/3)
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A scientist extracted 50.0 g oven-dry soil with 100 mL of deionized water. He transferred 50 mL of the extracts to a weight-known (35.2300 g) evaporation dish. After evaporation, the dish and the residues weighed 35.4815 g. The total dissolved salt content of the soil was
A. 25.15mg/g
B. 0.71 g/g
c. 10.06mg/g
D. 5.03mg/
Answers
The total dissolved salt content of the soil is approximately 10.06 mg/g.
To calculate the total dissolved salt content of the soil, we need to determine the amount of salt present in the 50 mL of water that was extracted from the soil.
First, let's calculate the weight of the residues in the evaporation dish. The initial weight of the dish is 35.2300 g, and the final weight after evaporation is 35.4815 g. Therefore, the weight of the residues is 35.4815 g - 35.2300 g = 0.2515 g.
Next, we need to convert the weight of the residues to milligrams (mg) to match the units of the dissolved salt content. The weight of the residues is 0.2515 g, which is equal to 251.5 mg.
Now, we can calculate the dissolved salt content per gram of soil. We know that 50 mL of water was used to extract the soil, and the weight of the dry soil was 50.0 g. So, the dissolved salt content per gram of soil is given by:
(251.5 mg / 50 mL) * (100 mL / 50.0 g) = 5.03 mg/g
Therefore, the correct answer is approximately 10.06 mg/g.
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