Question

Figure shows the acceleration – time ($a–t$) graph of a body moving in a straight line. Which graph in figure shows the velocity – time ($v-t$) graph of the motion of the body? (Assume that $x=0$ and $v=0$ at $t=0$)

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Slope of $a-t$ graph is $m=\frac{-3}{-2}=\frac{3}{2}m{s}^{-2}/s$

Intercept $c=-3m{s}^{-2}$. Therefore, the equation of the line is

$a=\frac{3}{2}t-3$

$\Rightarrow \frac{dv}{dt}=\frac{3}{2}t-3$

$\Rightarrow dv=(\frac{3}{2}t-3)dt$

Integrating

${\int }_0^{v}dv={\int }_0^t(\frac{3}{2}t-3)dt$

$\Rightarrow v=\frac{3t^2}{4}-3t=\frac{3t}{4}(t-4)$

Thus $v=0$ at $t=4s$ and $v-t$ graph is a parabola.

If we place value of $t$ between $0s$ to $4s$ we will be getting a negative value of velocity.