Question:

The position-time graph below represents the motion of a car.

a) Describe the motion of the car during the first 10 seconds.

b) Determine the average velocity of the car from t = 10 seconds to t = 20 seconds.

c) Calculate the displacement of the car during the time interval from t = 0 seconds to t = 20 seconds.

Answer:

a) During the first 10 seconds, the car is moving in a straight line at a constant positive velocity. This can be observed from the positive slope of the position-time graph within this time interval. The car is moving away from the origin (position = 0) in a consistent manner.

b) To determine the average velocity of the car from t = 10 seconds to t = 20 seconds, we need to calculate the change in position and divide it by the change in time.

Change in position = Final position - Initial position

The final position at t = 20 seconds is 40 meters, and the initial position at t = 10 seconds is 20 meters.

Change in position = 40 m - 20 m = 20 m

Change in time = Final time - Initial time

The final time is 20 seconds, and the initial time is 10 seconds.

Change in time = 20 s - 10 s = 10 s

Average velocity = Change in position / Change in time

Average velocity = 20 m / 10 s = 2 m/s

Therefore, the average velocity of the car from t = 10 seconds to t = 20 seconds is 2 m/s.

c) To calculate the displacement of the car during the time interval from t = 0 seconds to t = 20 seconds, we need to consider the change in position.

The initial position at t = 0 seconds is 0 meters, and the final position at t = 20 seconds is 40 meters.

Displacement = Final position - Initial position

Displacement = 40 m - 0 m = 40 m

Therefore, the displacement of the car during the time interval from t = 0 seconds to t = 20 seconds is 40 meters.