# 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 #11 : Mechanics Exam

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 #11 : Linear Motion

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 ### All AP Physics C: Mechanics Resources 