AP Physics 1 Exam Question

A car is traveling along a straight road. The following graph represents the car's velocity as a function of time.

Question: Based on the given graph, analyze the motion of the car and answer the following questions:

a) What is the initial velocity of the car at t=0 seconds? b) What is the acceleration of the car between t=2 seconds and t=6 seconds? c) How far does the car travel during the first 8 seconds? d) Does the car experience any constant velocity intervals? If yes, specify the time intervals. If no, explain why.

Answer:

a) To determine the initial velocity of the car at t=0 seconds, we look at the graph where the time axis intersects the velocity axis. From the graph, it can be observed that the velocity of the car at t=0 seconds is 0 m/s. Therefore, the initial velocity of the car is 0 m/s.

b) To determine the acceleration between t=2 seconds and t=6 seconds, we need to find the change in velocity and the change in time. On the velocity-time graph, we draw a straight line connecting the points at t=2 seconds and t=6 seconds. Using the slope formula, the change in velocity is given by:

change in velocity = (final velocity - initial velocity) = (30 m/s - 10 m/s) = 20 m/s

The change in time is given by:

change in time = (final time - initial time) = (6 s - 2 s) = 4 s

Then, the acceleration is given by:

acceleration = change in velocity / change in time = 20 m/s / 4 s = 5 m/s²

Therefore, the acceleration of the car between t=2 seconds and t=6 seconds is 5 m/s².

c) To find the distance traveled during the first 8 seconds, we need to calculate the area under the velocity-time graph for the time interval t=0 to t=8 seconds. This area represents the displacement or distance traveled. From the graph, the shape can be divided into two rectangles and a triangle.

Area of the rectangle on the left: Area = base × height = 2 s × 10 m/s = 20 m

Area of the triangle on the right: Area = 0.5 × base × height = 6 s × ((30 m/s - 10 m/s) / 2) = 6 s × 10 m/s = 60 m

Total distance traveled = Area of rectangle + Area of triangle = 20 m + 60 m = 80 m

Hence, the car travels a distance of 80 meters during the first 8 seconds.

d) The car experiences constant velocity intervals when the graph is a horizontal straight line. From the velocity-time graph, we can observe that the car experiences two constant velocity intervals: one between t=0 seconds and t=2 seconds, and another between t=8 seconds and t=10 seconds. In both intervals, the velocity remains constant at 10 m/s.

Therefore, the car experiences two constant velocity intervals: t=0s to t=2s and t=8s to t=10s.