Velocity, Speed, Acceleration

Practice Questions

AP Calculus BC › Velocity, Speed, Acceleration

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10 of 14

1

The equation $y=\frac{1}{2} t^4 +10t$ models the position of an object after t seconds. What is the acceleration at 3 seconds?

2

The position of an object is given by the equation $y = \frac{1}{3} t^3 - \frac{1}{2} t^2 -2t + 4$ . What is its acceleration at t = 2?

3

A particle's position on the -axis is given by the function $f(t)=\sin(t)-t+1$ from $0 < t <\pi$ .

When does the particle change direction?

4

A particle moves in space with velocity given by

$v(t)=\alpha t^3+\beta \sqrt{t}$

where $\alpha, \beta$ are constant parameters.

Find the acceleration of the particle when t=4.

5

The velocity of a particle is given by v(t). Find the particle's acceleration when t=3.

6

The equation $y= \sin (2t)$ models the position of an object after t seconds. What is its speed after $\pi$ seconds?

7

The velocity of a particle is given by v(t). Find the function which models the particle's acceleration.

8

Find the first and second derivatives of the function

9

Find the velocity function from an acceleration function given by

and the condition

10

Find the velocity function of the particle if its position is given by the following function:

$s(t)=e^t\tan(t)+t^5+3$

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