Question

The area under the acceleration-time graph between any two instants $t=t_1$ and $t=t_2$ gives the velocity gained/lost in time $\delta t=t_2-t_1$ if :

• 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

acceleration is given as $a=\frac{dv}{dt}$...(i)

Integrating equation (i)

$v={\int }_{t_1}^{t_2}adt$ irrespective of anything.