Question

The distance-time graph of a body is a straight line inclined to the time axis. The body is in
A. Uniform motion
B. Uniformly accelerated motion
C. Uniformly retarded motion
D. Rest position

Answer 1

Hint: For the body in the uniform motion, the acceleration of the body should be zero. Use the formula for average velocity to express the velocity of the body. The slope of the distance-time graph represents the average velocity of the body.

Complete step by step solution:
We have given that the distance-time graph of a body is inclined to the time axis. Therefore, we can draw the distance-time graph as shown in the figure below.

From the above graph, the slope of the line is,
\[\dfrac{{{x_2} - {x_1}}}{{{t_2} - {t_1}}} = \dfrac{{\Delta x}}{{\Delta t}}\]
From the above graph, we can say that the slope is constant since the line is a straight line passing through the origin.
We know that the body is said to be in the uniform motion, if the acceleration of the body is zero.
We have, the average velocity of the body is,
\[{v_{avg}} = \dfrac{{{x_2} - {x_1}}}{{{t_2} - {t_1}}}\]
Here, \[{x_2}\] is the final position,\[{x_1}\] is the initial position of the body and t represents time.
We have seen that the term on the right hand side is the slope of the line and it is constant, therefore, the velocity of the body is also constant. Since the velocity is constant, the body has zero acceleration. Therefore, we can say that the body has uniform motion.
So, the correct answer is option (A).
The acceleration of the body shown in the above distance-time graph is zero. Therefore, the body cannot have uniformly accelerated motion. Thus, the option (B) is incorrect.
The acceleration of the body shown in the above distance-time graph is zero. Therefore, the body cannot have uniformly retarded motion. Thus, the option (C) is incorrect.

We know that for a body in rest position, the distance-time graph does not incline to the time axis rather than overlap on the time axis. Therefore, the option (D) is incorrect.

So, the correct answer is “Option A”.

Note:
In the formula for average velocity, \[{t_2} - {t_1}\] is not the difference in the time but it is the total elapsed time. If you have given the velocity-time graph, then for uniform motion of the body, the graph will be parallel to the time axis.