Question

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

• 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 velocity again when,
$A_1+A_2=0\Rightarrow |A_1|=|A_2|$
$A_1=\frac{1}{2}\times 10\times 4=20$
$A_2=\frac{1}{2}\times (t_o-4)\times (-x)=20$
$\begin{array}{}\Rightarrow x(t_o-4)=40& \text{(1)}\end{array}$
Since the slope of line remains same,
$\begin{array}{}\therefore \frac{10}{4}=\frac{-x}{t_o-4}& \text{(2)}\end{array}$
Solving $\left(1\right)$ and $\left(2\right)$, we get
$x=-10$ and $t_o=8\text{s}$
Hence particle will acquire its initial velocity at $8\text{s}$