Question

The velocity-time graph is given as


The most probable acceleration-time graph is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

From given $v-t$ curve, $v$ is depending on time parabolically and parabola is symmetric about $v-axis$ so, we can say that $v\propto t^2$ or $v=k{t}^2$, where $k$ is any constant
$\therefore \frac{dv}{dt}=a\Rightarrow a=\frac{d\left(k{t}^2\right)}{dt}\Rightarrow a=2kt$

i.e. $a$ is proportional to $t$ and after that velocity is constant i.e. acceleration becomes zero. So, the graph (b) is most probable graph