Question

The velocity-time graph for a body with non-uniform motion (assume non-constant acceleration) is a:
A. Straight line making some angle with the positive X axis.
B. Straight line parallel to X-axis.
C. Straight line parallel to Y-axis.
D. Curved line.

Answer 1

Hint:- In this question, we have to find the different conditions for different types of graphs. A particular graph can be made for a particular condition i.e. the graph of a straight line making some angle with the positive X axis will be possible for constant acceleration.

Complete step-by-step solution :
We know that the displacement time graph gives the velocity of the body in a particular direction. Similarly, the velocity time graph gives the acceleration of that body in a particular direction.
We can explain the possibility of a graph according to the given options in the question.
In the first option, it is given that the graph may be straight line making some angle with the positive X-axis. This graph can be possible when the acceleration is constant throughout the motion. This type of motion should be uniform motion. The slope of this type of graph is the same at every point of the motion.
In the second option, it is given that the graph may be a straight line parallel to the X-axis. This graph can be possible only if the acceleration is zero. But according to the question, the body has non constant acceleration.
In the third option, it is given that the graph may be a straight line parallel to the Y-axis. This graph can’t be possible for a velocity time graph as the Y-axis represents the velocity and it is not possible that for a constant time, the velocity has changed.
In the fourth option, it is given that the graph may be a curved line. This graph can be possible when the acceleration is variable throughout the motion.
So, the velocity-time graph for a body with non-uniform motion and non-constant acceleration is a curved line.
Hence option D is correct.

Note:- We have to keep in mind that the displacement time graph gives velocity and the velocity time graph gives acceleration. In a non-constant acceleration, the slope is different at different points.