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 in the figure below. When the car changes speed it does so uniformly. Select the appropriate choice for each statement.

The x-acceleration is ..... zero at 36 sec.

At 73 sec, the speed is as high as it gets.

The x-acceleration is ..... zero at 20 sec .

The acceleration magnitude at 36 sec is ..... the acceleration magnitude at 15 sec.

The speed at 73 sec is ..... the speed at 4 sec.

The speed is ..... zero at 26 sec.

Using the graph above, calculate the average speed of the car for the period from 0 to 30.0 s

Explanation / Answer

part 1:

at 36 seconds, the distance is constant with respect to time.

==> speed is slope of the distance vs time graph.
==> speed is zero at 36 seconds.
==> acceleration is slope of speed vs time graph.
==> acceleration is equal to zero at 36 sec.

part 2:

speed is slope of distance vs time curve.

so speed is maximum when the slope is maximum.

from the graph , it can be seen that slope is maximum between 40 to 60 seconds.

so the statement "at 73 sec, the speed is as high as it gets" is false.

part 3:

at 20 seconds, the distance is constant with respect to time.

==> speed is slope of the distance vs time graph.
==> speed is zero at 20 seconds.
==> acceleration is slope of speed vs time graph.
==> acceleration is equal to zero at 20 sec.

part 4:

as speed is constant between 0 to 18 seconds and speed is zero at 36 seconds.

in both cases the acceleration is zero.

hence acceleration magnitude at 36 seconds is same as acceleration magnitude at 15 sec.

part 5:

at 73 seconds, the slope is lesser than slope at 4 seconds.

then speed at 73 sec is smaller than speed at 4 sec.

part 6:

at 26 seconds, distance is constant

==> speed is zero.

part 7:

from 0 to 30, the distance covered is 300 m

==> acerage speed=total distance/total time=300/30=10 m/s

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