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AP Physics C: Mechanics : Understanding Accelerations

Study concepts, example questions & explanations for AP Physics C: Mechanics

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Example Questions

Example Question #11 : Linear Motion

a(t)=6t^2

A car undergoes acceleration according to the given function. What distance has the car traveled after three seconds?

Possible Answers:

40.5m

60m

54m

24m

48.5m

Correct answer:

40.5m

Explanation:

We can determine the velocity by taking the second integral of acceleration for the time interval of 0s to 3s.

$\int a(t)dt = v(t)$

$\int_{0}^{3}\int a(t)dt^2 = x(3) - x(0)$

Solve for the first integral.

$\int_{0}^{3}\int a(t)dt^2 =\int_{0}^{3}(6t^2)\int dt^2=\int_{0}^{3}(2t^3)dt$

Solve for the second integral, using the time interval.

$\int_{0}^{3}(2t^3)dt = \frac{(3)^4}{2}-\frac{(0)^4}{2} = \frac{81}{2} = 40.5m$

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Example Question #11 : Mechanics Exam

a(t)=6t^2

A car undergoes acceleration according to the given function. How fast is the car moving after four seconds?

Possible Answers:

$144\frac{m}{s}$

$81\frac{m}{s}$

$128\frac{m}{s}$

$48\frac{m}{s}$

$64\frac{m}{s}$

Correct answer:

$128\frac{m}{s}$

Explanation:

We can find the car's velocity by taking the integral of the acceleration function during the given time interval.

$v(t) = \int a(t)\,dt$

$v(4) = \int_{0}^{4} a(t)\,dt = \int_{0}^{4} (6t^2)\,dt$

Solve the integral for the time interval of 0s to 4s. This will give us the final velocity.

$\int_{0}^{4} (6t^2)\,dt = 2(4)^3+2(0)^3 = 128\ \frac{m}{s}$

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Example Question #11 : Linear Motion

a(t)=6t^2

A car undergoes acceleration according to the given function. If the threshold for serious injury or fatality for a human undergoing horizontal acceleration is 60 gees (1 gee = 10 meters per second per second), how long would a human be able to withstand riding in this car?

Possible Answers:

10s

25s

60s

100s

Correct answer:

10s

Explanation:

Calculate the maximum acceration in meters per second.

$a(t) = 6t^2 = 60\ gees = 600\ \frac{m}{s^2}$

Solve for the time.

$a(t)=6t^2=600\frac{m}{s^2}$

100 = t^2

$t = 10\ s$

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Example Question #1 : Understanding Accelerations

A ball travels with a velocity as described by the function below:

v(t) = 5

What is the ball's acceleration?

Possible Answers:

$0\frac{m}{s^2}$

$-1 \frac{m}{s^2}$

$-5 \frac{m}{s^2}$

$5 \frac{m}{s^2}$

$1\frac{m}{s^2}$

Correct answer:

$0\frac{m}{s^2}$

Explanation:

Acceleration is equal to the derivative of the velocity function.

$a(t) = \frac{dv(t)}{dt}$

Since the velocity is constant, the derivative will be equal to zero.

$\frac{d}{dt}(5) = 0$

The acceleration is equal to zero.

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All AP Physics C: Mechanics Resources

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AP Physics C: Mechanics : Understanding Accelerations

Study concepts, example questions & explanations for AP Physics C: Mechanics

All AP Physics C: Mechanics Resources

Example Questions

Example Question #11 : Linear Motion

Example Question #11 : Mechanics Exam

Example Question #11 : Linear Motion

Example Question #1 : Understanding Accelerations

All AP Physics C: Mechanics Resources

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