Question

FIGURE Q2.8 shows six frames from the motion diagrams of two moving cars, A and B.

a. Do the two cars ever have the same position at one instant of time? If so, in which frame number (or numbers)?

b. Do the two cars ever have the same velocity at one instant of time? If so, between which two frames?

Short answer

a. No, the two cars cannot have the same position at one instant of time.

b. Yes, between the 4th and 6th frame, velocity of the both cars A and B is same.

Step-by-step solution

Part (a) Step 1: Introduction

The motion of two cars A and B are shown in 6 frames or in 6 different positions.

Position-time graph for the motion of two cars

The position-time graph for a set of 6 frames for a time range of 0-5 sec is shown below:

Therefore, from the graph it is clear that the position graph of the two cars A and B never intersect at a point. So the two cars can never be at a same position at any instance.

Part (b) Step 1: Given information

Six different frames from the motion diagram of car A and B are given in the question. We have to compare their velocities.

Explanation through speed-time graph

The speed-time graph for the motion of the car A should be parallel to time axis as the position graph shows that the car A has a uniform speed. The car B has a non-uniform speed.

At time $t=4s$, the speed of the two cars A and B intersects at a point. That means between the 4th and 6th frame, velocity of the both cars A and B is same.