A car travels a certain distance along a straight road (in the +x direction). Th

Question

A car travels a certain distance along a straight road (in the +x direction). The distance the car travels as a function of time is shown the figure below. When the car changes speed it does so uniformly. Select the appropriate choice for each statement. The acceleration magnitude at 15 sec is ..... the acceleration magnitude at 36 sec. At 4 sec, the speed is as high as it gets. The x-acceleration is ..... zero at 10 sec. The x-acceleration is ..... zero at 15 sec. The speed is ..... zero at 23 sec. The speed at 64 sec is ..... the speed at 4 sec. Using the graph above, calculate the average speed of the car for the period from 0 to 60.0 s

Explanation / Answer

The given graph is a distance vs time graph. Thus the slope of the graph will signify the velocity of the car.

1] Acceleration of the car at 15s is equal to the acceleration at 36s and is equal to zero since the velocity is constant at these two points.

2] At 4s, the car is moving with a constant velocity but this velocity is not the greatest as the car is travelling at a higher velocity between 40s < t < 60s.

[we know this because the slope of the graph there is more than the slope of the graph in the region 0 < t < 20s.

3] The x acceleration is equal to zero at 4s since the velocity is constant.

4] The x acceleration is equal to zero at 15s since the velocity is constant.

5] The speed is equal to zero at 23s since the slope is zero at 23s.

6] The speed at 64s is equal to the speed at 4s since the slope of the graph is same [hence same velocities].

Average speed of car between 0s to 60s will be:

v = (1000 - 0)/(60 - 0) = 16.67 m/s.

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