### All Calculus 1 Resources

## Example Questions

### Example Question #341 : How To Find Acceleration

The position of a is given by the following functions:

Find the acceleration.

**Possible Answers:**

Answer not listed

**Correct answer:**

In order to find the acceleration of a certain point, you first find the derivative of the position function to get the velocity function and the derivative of the velocity function to get the acceleration function:

In this case, the position function is:

Then take the derivative of the position function to get the velocity function:

Then take the derivative of the velocity function to get the acceleration function:

Then, plug into the acceleration function:

Therefore, the answer is:

### Example Question #342 : How To Find Acceleration

Given the position function of an object in motion (in meters), find the acceleration of the object at t=2 seconds.

**Possible Answers:**

-4.9 m/s/s

9.8 m/s/s

-9.8 m/s/s

4.9 m/s/s

None of the other answers.

**Correct answer:**

-9.8 m/s/s

The acceleration of an object in motion at any given time is modeled by the second derivative of its position function. That is

The acceleration of the object at t=2 seconds is then

In this case, the acceleration is constant across all values of t.

### Example Question #343 : How To Find Acceleration

Find the acceleration of a particle at given the following velocity function:

**Possible Answers:**

**Correct answer:**

The first step is to obtain the acceleration equation.

This is done by taking the first derivative of the velocity function,

using the power rule,

.

The acceleration equation

can be used to find the acceleration at any given time.

In our case, plugging in 5 for t into the equation gives,

.

### Example Question #344 : How To Find Acceleration

Find the acceleration of a particle given its velocity function is .

**Possible Answers:**

**Correct answer:**

The acceleration function can be found given any velocity function by taking its derivative.

Using the power rule

,

the derivative becomes,

.

Recall that the derivative of a constant is always zero.

### Example Question #341 : How To Find Acceleration

Find the acceleration function of a car who's velocity function is given by .

**Possible Answers:**

**Correct answer:**

The derivative of the velocity function is acceleration, and using the power rule

,

you get

.

Recall that the derivative of a constant is zero.

Certified Tutor