# AP Physics C: Mechanics : Calculating Motion in One Dimension

## Example Questions

### Example Question #1 : Calculating Motion In One Dimension

A man runs with a velocity as described by the function below.

How far does he travel in 1 minute?

Explanation:

Distance is given by the integral of a velocity function. For this question, we will need to integrate over the interval of 0s to 60s.

### Example Question #1 : Calculating Motion In One Dimension

A man runs with a velocity described by the function below.

What is the function for his acceleration?

Explanation:

The function for acceleration is the derivative of the function for velocity.

### Example Question #2 : Calculating Motion In One Dimension

A particle traveling in a straight line accelerates uniformly from rest to  in  and then continues at constant speed for an additional for an additional . What is the total distance traveled by the particle during the ?

Explanation:

First off we have to convert  to meters per second.

Next we have to calculate the distance the object traveled the first 5 seconds, when it was starting from rest. We are given time, initial speed to be . The acceleration of the object at this time can be calculated using:

, substituting the values, we get:

Next, we use the distance equation to find the distance in the first 5 seconds:

because the initial speed is .

If we plug in , , we get:

Next we have to find the distance the the object travels at constant speed for 3 seconds. We can use the equation:

in this case is not equal to , it is equal to and

Plugging in the equation, we get

Adding  and  we get the total distance to be