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 velocity? (in seconds)

• A. $12$
• B. $5$
• C. $8$
• D. $16$

Answer 1

Answer: (C)

$8$

The area under the velocity-time graph represents the change in velocity

Let at time $t_0$ the particle acquire the initial velocity

$\therefore$ change in velocity of the particle in time $t_0$ is zero i.e., under a v/s t graph is zero

or $\frac{1}{2}OA\times OB=\frac{1}{2}BC\times CD$

$OB\tan \theta \times OB=CD\tan \theta CD$

${\left(OB\right)}^2={\left(CD\right)}^2$

$\therefore OB=CD$

or $4=t_0-4$

$t_0=8$

So at time $t=8$sec particle acquires its initial velocity