### All Calculus 1 Resources

## 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?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

.

**Possible Answers:**

**Correct answer:**

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

.

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

None of the other answers

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

Take the first derivative by using the Power Rule () of :

Using the Power Rule again, find the second derivative of :