Question

The acceleration-time graph of a body is shown below


The most probable velocity time graph of the body is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

From given a-t graph acceleration is increasing at constant rate
$\therefore \frac{da}{dt}=k\left(\text{constant}\right)\Rightarrow a=kt$ (by integration)

$\Rightarrow \frac{dv}{dt}=kt\Rightarrow \int dv=\int ktdt\Rightarrow v=\frac{k{t}^2}{2}$

i.e. $v$ is depending on time parabolically and parabola is symmetric about $v$ axis. After a certain point, acceleration becomes zero i.e. velocity becomes constant.
Hence (c) is the most probable graph.