Question

A particle starts from rest at $t=0s$ and undergoes an acceleration $a$ in $m{s}^{-2}$ with time $t$ in seconds which is shown in figure. Which one of the following plot represents velocity $v$ in $m{s}^{-1}$ versus time $t$ in second?

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

From $a-t$ graph, we observe that

For $t=0s$ to $t=2s;a$ is positive, i.e. $a>0$. So, $v-t$ graph will be a straight line with positive slope. For $t=2s$ to $t=4s,a$ is negative $(a<0)$, so $v-t$ graph will be a straight line with negative slope. Complete $v$ - $t$ graph will be as below.

Also, $v=$ Area under $a-t$ graph for $t=0s$ to $t=2s$ $=3\times 2$
$\Rightarrow v=6m{s}^{-1}$, which is the maximum velocity attained.
This is shown in graph .