Question

What is the nature of the displacement-time graph of a body moving with constant acceleration?

Answer 1

Displacement – Time graph of a body moving with constant acceleration is as shown in the right side.

Explanation: 

Slope of displacement – time graph gives the velocity. 

Consider the following graph:

Here AB = Displacement of Body 

And OB = Time Taken 

Now, Velocity = \(\frac{AB}{OB}\)

But \(\frac{AB}{OB}\)is known as slope of line OA. 

We know that in constant acceleration, velocity is changing with time at a constant rate. 

Since,Acceleration = \(\frac{Change\,in\,velocity}{time}\)

So, slope of displacement – time graph is changing at a constant rate and hence we get a graph like shown at the beginning.