Question

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

Answer 1

Given,

An Acceleration time graph,

So, the area under the velocity time graph shows the change in velocity,

Let the time $t_0$ the particle accuire the initial velocity,

Therefore the change in velocity of the particle in the time $t$ is:

So, Area under the velocity time graph is zero.

Thus Area of $△AOB=areaof△BCD$

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

$O{B}^{2}tan\theta =C{D}^{2}tan\theta$

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

$4=t_0-4$

$t_0=-8$