Question

The area under the velocity-time graph between any two instants $t=t_1$ and $t=t_2$ gives the displacement in time $\delta t=t_2-t_1$ :

• A. only if the particle moves with a uniform velocity
• B. only if the particle moves with a uniform acceleration
• C. only if the particle moves with an acceleration increasing at a uniform rate
• D. in all cases irrespective of whether the motion is one of uniform velocity, or of uniform acceleration or of variable acceleration

Answer 1

The correct option is D in all cases irrespective of whether the motion is one of uniform velocity, or of uniform acceleration or of variable acceleration

In general the area under the velocity-time graph gives the displacement happening in given time.
The area under the velocity-time graph between any two instants $t=t_1$ and $t=t_2$ gives the displacement in time $\delta t=t_2-t_1$.
This holds good for objects in uniform velocity, uniform acceleration, variable acceleration.