Question

A particle starts from rest at time $t=0$ and moves on a straight line with acceleration as plotted in figure. The speed of the a particle will be maximum at time

• A. $1\text{s}$
• B. $2\text{s}$
• C. $3\text{s}$
• D. $4\text{s}$

Answer 1

The correct option is B $2\text{s}$

Area under $a-t$ curve gives change in velocity.
From $t=0$ to $t=2$ seconds
Area under the $a-t$ curve $=-10\times 2=-20\text{m/s}$
$\Rightarrow \Delta v=v_2-v_0=-20\text{m/s}$
$\Rightarrow v_2=-20\text{m/s}$ ( velocity is in negative direction)
So, the body is speeding up from $t=0$ to $t=2\text{s}$
From $t=2$ to $t=4$ seconds
Area under the the $a-t$ curve = $10\times 2=20\text{m/s}$
$\Rightarrow \Delta v=v_4-v_2=20\text{m/s}$
$\Rightarrow v_4=0$
So, the body is speeding down from $t=2$ to $t=4$ seconds
Hence, the maximum velocity of the particle is at $t=2\text{s}$.