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 A

Given $\text{a}-\text{t}$ graph shows that acceleration is increasing at constant rate
Therefore,
$\frac{\text{da}}{\text{dt}}=\text{k}$(constant)
$\text{a}=\text{kt}$ (by integration) $\dots \left(i\right)$
As we know,
$\text{a}=\frac{\text{dv}}{\text{dt}}$
Put the value of a in $\left(i\right)$ equation we get
$\frac{\text{dv}}{\text{dt}}=\text{kt}$
$\text{dv}=\text{ktdt}$
Integrating both sides we get,
$\int \text{dv}=\text{k}\int \text{t}\text{dt}$
$\upsilon =\frac{{\text{kt}}^2}{2}\dots \left(ii\right)$
Equation $\left(ii\right)$ shows $v$ is dependent on time parabolically and parabola is symmetric about $v-$axis then suddenly acceleration becomes zero, i.e., velocity becomes constant.

Final Answer: (c)