All AP Physics C: Mechanics Resources
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?
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 #2 : Calculating Motion In One Dimension
A man runs with a velocity described by the function below.
What is the function for his acceleration?
The function for acceleration is the derivative of the function for velocity.
Example Question #3 : 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 ?
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