Question

The acceleration-time graph of a particle is as shown. at what time the particle acquires its initial velocity?

Answer 1

Answer: The final velocity will be equal to the initial velocity at t= 8 s.

Explanation:

We know that,

The equation of line

$y = mx+c$

According to figure

$\dfrac{t}{4}+\dfrac{a}{10}=1$

$10t+4a=40$

$a = 10-\dfrac{5}{2}t$

We know that,

The velocity is

$\dfrac{dv}{dt}=a$

On integrating$v = \int adt$

$v = \int 10-\dfrac{5}{2}t\ dt$

$v = 10t-\dfrac{5}{4}t^2+u$

Here, u = initial velocity

Now, when v = u then the time will be

$10t-\dfrac{5}{4}t^2=0$

$t = 8 sec$

Hence, The final velocity will be equal to the initial velocity at t= 8 s.