# Calculus 1 : How to find acceleration

## Example Questions

### Example Question #111 : How To Find Acceleration

An apple rolls off of a table. It's position is given by the following:

What is the acceleration of the apple?

Explanation:

Take the second derivative of  by using the Power Rule  twice .

Applying the power rule once will give us our velocity function,

.

Applying the power rule a second time results in our acceleration function,

.

Therefore, the acceleration of the apple is .

### Example Question #112 : How To Find Acceleration

A boulder rolls into a valley. Its position is given by , where  represents distance in yards and  represents time in seconds.

What is the acceleration of the boulder at ?

Explanation:

Take the second derivative by using the Power Rule  of ,

.

Applying the power rule a second time we find the acceleration function,

.

### Example Question #113 : How To Find Acceleration

Lola tosses an acorn into the lake. The position of the acorn is represented by , where  represents distance in feet and  represents time in seconds.

What is the acceleration of the acorn?

Explanation:

Take the second derivative by using the Power Rule  of ,

.

Applying the power rule again we find our acceleration function,

.

### Example Question #114 : How To Find Acceleration

Sian tosses an apple into the air. Its position is represented by , where  represents distance in feet and  represents time in seconds.

What is the acceleration of the apple?

Explanation:

Take the second derivative by using the Power Rule  of ,

.

Applying the power rule again we get the acceleration function,

.

### Example Question #115 : How To Find Acceleration

Piper throws a softball. Its position is represented by , where  represents distance in meters and  represents time in seconds.

What is the acceleration of the softball?

Explanation:

Take the second derivative by using the Power Rule  of ,

.

Applying the power rule a second time we find the acceleration function,

.

### Example Question #116 : How To Find Acceleration

Find the acceleration function

if

.

Explanation:

In order to find the acceleration function from the position function we need to take the second derivative of the position function.

When taking the derivative, we will use the power rule which states

and by applying this rule to each term we get

.

Next we find the second derivative,

.

Hence,

.

### Example Question #117 : How To Find Acceleration

Find  if

.

Explanation:

In order to find the acceleration function from the velocity function we need to take the derivative of the velocity function.

When taking the derivative, we will use the power rule which states

and by applying this rule to each term we get

.

As such,

.

Finally, to solve for  we set  to get

.

### Example Question #118 : How To Find Acceleration

A particle is moving according to the following equation:

What is the acceleration of the particle at the point ?

Explanation:

The position function of the particle is given as follows:

The first derivative of the position function describes the velocity of the particle:

This derivative was found by using the power rule , the derivative of x=1, and the derivative of a constant equaling zero.

The second derivative of the function - the derivative of the first derivative of the position function - describes the acceleration of the particle:

The derivative was found by the derivative of x=1, and the derivative of the constant equaling zero.

Thus, the acceleration of the particle is 4.

### Example Question #119 : How To Find Acceleration

A spaceship is traveling from Venus to Mercury according to the following equation:

Find the acceleration of the spaceship at .

Explanation:

The acceleration of the spaceship is given by the second derivative of the position equation.

The first derivative - which describes the velocity of the spaceship - is given by

.

This derivative was found using the power rule This derivative was found by using the power rule

The derivative of this function (the second derivative of the initial function)- the acceleration of the spaceship - is given by

.

This derivative was also found using the power rule, and the rule that the derivative of a constant (in this case, 56) equals zero.

At , the acceleration

.

### Example Question #120 : How To Find Acceleration

A paper airplane flies across a room. It's position is represented by , where  represents distance in feet and  represents time in seconds.

What is the acceleration of the airplane?