Question

The acceleration- time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial speed?

• A. $12\text{s}$
• B. $5\text{s}$
• C. $8\text{s}$
• D. $16\text{s}$

Answer 1

The correct option is C $8\text{s}$

We know that under area under $a-t$ graph represents change in velocity.
Let $A_1$ and $A_2$ be the areas of upper and lower triangle respectively.

Particle will acquire the initial speed again when,
$A_1+A_2=0$
$\Rightarrow \frac{1}{2}\times 10\times 4+\frac{1}{2}\times (t_o-4)\times -10=0$
$\Rightarrow t_o=8\text{s}$
At this time direction of velocity will be opposite but the magnitude will be equal.