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.

It wont let me post the photo of the graph for some reason, so here is a link to it https://d2vlcm61l7u1fs.cloudfront.net/media%2Fa8f%2Fa8f89426-1896-44e8-863a-df989e927825%2FphpeLSO6i.png

The acceleration magnitude at 15 sec is ..... the acceleration magnitude at 37 sec.

The x-acceleration is ..... zero at 7 sec .

The x-acceleration is ..... zero at 58 sec. \

The speed at 64 sec is ..... the speed at 10 sec.

At 64 sec, the speed is as high as it gets.

The speed is ..... zero at 29 sec.

Answer 1

1) In distance vs time graph. Magnitude of acceleration is given by curvature of the graph. If the curvature is more then it has more acceleration. In the given graph, the curvature at 15 seconds is more than curvature at 37 seconds. Therefore the acceleration magnitude at 15 sec is greater than the acceleration magnitude at 37 sec.

2) In distance vs time graph, the slope of straight line gives the speed of object. If the straight line is more steep, it has more speed. If the straight line is parallel to time axis, its speed is zero. In the given graph, at 7 sec, the speed is decreasing( as the slope is becoming less and less steep). Therefore acceleration is opposite to velocity, so acceleration is less than zero.

3) In the given graph, at 58 sec, the speed is increasing. Therefore acceleration is more than zero.

4) At 64 sec, the slope is less steeper compared to slope of other straight lines. Therefore the given statement is false

5) At 29 sec, since the line is parallel to time axis, speed is zero. Therefore, the speed is equal to zero at 29 sec.