Question

The area under the velocity-time graph between any two instant $t=t_1$ and $t=t_2$ gives the displacement covered in time $\delta t=t_2-t_1$. This is true:

• 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

Answer: (D)

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

The area under the velocity-time graph between any two instant $t=t_1$ and $t=t_2$ gives the distance covered in time $\delta t=t_2-t_1$.
1. Straight line parallel to time-axis - uniform motion
2. Straight line inclined to the time-axis - non-uniform motion
Thus, area under $v-t$ graph gives displacement for motion in uniform velocity, uniform acceleration, variable acceleration.