Chapter 2.3, Problem 28R

To determine

To describe:the line that would be needed to plot on a speed-time graph for the motion of a car and the line that is required to draw on a distance-time graph.

Explanation of Solution

Introduction:

A horizontal line on a speed-time graph represents a constant speed and a sloping line on the same graph denotes acceleration. From the distance-time graph, one would get the speed of an object.

The equation of motion is,

  $v=u+at$.............(1)

Here, $v,u$ , $t$ and $a$ are final velocity, initial velocity, time, and acceleration.

Rearranging the equation (1),

  $a=\frac{v-u}{t}$.............(2)

From the above equation (2), it is found that the acceleration is increasing which indicates an object moving from rest to top speed. The distance-time graph shows a rise in the distance with the run of time. After attaining the top speed, the acceleration becomes zero and the distance covered by the object in equal interval of time would be the same resulting in constant velocity or speed.

Conclusion:

Hence,the distance-time graph shows a rise in the distance with the run of time, and the line in the distance-time graph shows constant velocity/speed.