# Calculus 1 : How to find acceleration

## Example Questions

### Example Question #21 : How To Find Acceleration

What is the acceleration function when the velocity function is

?

Explanation:

Since the velocity function is . The acceleration function is also , since the derivative of  is .

Therefore,

.

### Example Question #5 : Calculus Review

If  models the distance of a projectile as a function of time, find the acceleration of the projectile at .

Explanation:

We are given a function dealing with distance and asked to find an acceleration. recall that velocity is the first derivative of position and acceleration is the derivative of velocity. Find the second derivative of h(t) and evaluate at t=6.

### Example Question #22 : How To Find Acceleration

Function  gives the velocity of a particle as a function of time.

Find the equation that models that particle's acceleration over time.

Explanation:

Recall that velocity is the first derivative of position, and acceleration is the second derivative of position. We begin with velocity, so we need to integrate to find position and derive to find acceleration.

To derive a polynomial, simply decrease each exponent by one and bring the original number down in front to multiply.

So this

Becomes:

So our acceleration is given by

### Example Question #23 : How To Find Acceleration

Function  gives the velocity of a particle as a function of time.

Find the acceleration (in meters per second per second) of the particle at  seconds.

Explanation:

Recall that velocity is the first derivative of position, and acceleration is the second derivative of position. We begin with velocity, so we need to integrate to find position and derive to find acceleration.

To derive a polynomial, simply decrease each exponent by one and bring the original number down in front to multiply.

So this

Becomes:

So our acceleration is given by

Now, to find the acceleration at 5 seconds, we need to plug in 5 for t

### Example Question #24 : How To Find Acceleration

Consider the velocity function modeled in meters per second by .

Find the accelaration after  seconds of a particle whose velocity is modeled by .

Explanation:

Recall that acceleration is the first derivative of velocity. So, to find acceleration we need to find and evaluate the following:

So, if

Then,

So our acceleration is .

### Example Question #25 : How To Find Acceleration

Consider the following position function:

Find the acceleration after  seconds of a particle whose position is given by .

Explanation:

Recall that acceleration is the second derivative of position, so we need p''(7).

Taking the first derivative we get:

Taking the second derivative and plugging in 7 we get:

So our acceleration after 7 seconds is

.

### Example Question #26 : How To Find Acceleration

Given that the position of a particle is known  to be:

Find the acceleration of the particle.

Explanation:

To find the expression of the acceleration we need to differentiate the expression of the position vector twice with respect to time.

Note that we do differentiation componentwise.

We have the following:

.

We differentiate one more time:

and the third component is simply zero since it is a constant.

This gives us the expression for the acceleration.

### Example Question #27 : How To Find Acceleration

A planet is moving along the path:

What is its acceleration?

Explanation:

To find the correct expression of the acceleration, we will need to differentiate the expression of the position twice with respect to time.

We recall the following:

and

This gives us

### Example Question #28 : How To Find Acceleration

Assume that a particle is moving along the path given by the equations :

What is the acceleration of the particle?

Explanation:

To find the expression of the acceleration we need to find the second derivative of each of the components with respect to time.

Note that we have the following:

The first component is zero since its second derivative is zero.

This gives the required expression.

### Example Question #29 : How To Find Acceleration

Given the vector position:

Find the expression of the velocity.