Calculate Position, Velocity, and Acceleration

Practice Questions

Calculus AB › Calculate Position, Velocity, and Acceleration

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1

Given the velocity function

$v(x)=\int_{0}^{x^2+2x+1} z^d\sin(z^5) dz$

where is real number such that $d\in [0,1]$ , find the acceleration function

.

2

Given the velocity function

$v(x)=\int_{0}^{x^2+2x+1} z^d\sin(z^5) dz$

where is real number such that $d\in [0,1]$ , find the acceleration function

.

3

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

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

4

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

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

5

Let

$f(x)=e^{\pi x}$

Find the first and second derivative of the function.

6

Let

$f(x)=e^{\pi x}$

Find the first and second derivative of the function.

7

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?

8

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?

9

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

10

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

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