Question

FIGURE Q2.5 shows a position-versus-time graph for the motion of

objects A and B as they move along the same axis.

a. At the instant t = 1 s, is the speed of A greater than, less than,

or equal to the speed of B? Explain.

b. Do objects A and B ever have the same speed? If so, at what

time or times? Explain.

Short answer

(a) At time $t=1s$, speed of object A is greater than the speed of object B.

(b) At time$t=2.5s$, speed of object A and B are the same.

Step-by-step solution

Part (a) Step 1: Introduction

A graph showing motion of two particles A and B having uniform and non-uniform motion is given in this question.

Explanation

At $t=1s$, consider the slope of the path of motion of particle B as:

The slope of speed of particle B at the instance of time is zero and there is a positive slope of the speed of particle A.

Therefore, at time $t=1s$, speed of object A is greater than the speed of object B.

Part (b) Step 1: Introduction

The two objects A and B shown in the given problem have a position-time graph. We have to determine if the two objects have same speed at any instant.

Explanation

If we draw a slope on the graph of the motion of object B, it will determine the speed of the object at that time. If at any instance of time, the slope of the graph of both A and B are parallel to each other then their velocity will be same.

Speed determination

We can compare the speed of the two objects by the following diagram:

So the speed of object B is same as that of object A at time $t=2.5s$ as at this time, velocity slopes of both the objects are the same.