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

Answer: (C)

From given $a-t$ graph acceleration is increasing at constant rate
$\therefore \frac{da}{dt}=k$ (constant)
$\Rightarrow a=kt$ (by integration)
$\Rightarrow \frac{dv}{dt}=kt\Rightarrow dv=ktdt$
$\Rightarrow \int dv=k\int tdt\Rightarrow v=\frac{k{t}^2}{2}R$
i.e., $v$ is dependent on time parabolically and parabola is symmetric about $v$-axis and suddenly acceleration becomes zero. i.e., velocity becomes constant. Hence the most stable graph is (c).