Question

Acceleration time graph for particle moving along x axis from rest is shown in figure if initial velocity of particle is -5m/s then velocity at time t=8 sec is

Answer 1

as you know, acceleration is the rate of change of velocity. e.g., $a=\frac{\Delta{v}}{\Delta{t}}$
when $\Delta{t}\to 0$
then, $a=\displaystyle\lim_{\Delta{t}\to 0}\frac{\Delta{v}}{\Delta{t}}=\frac{dv}{dt}$

so, a = dv/dt $\implies\int{dv}=\int{a}\,dt$
it means, if acceleration time graph is given then area enclosed by acceleration time graph shows change in velocity of particle.

so, ∆v = area enclosed by acceleration - time graph
v - u = 1/2 × 10 × 6 - 1/2 × 10 × (8 - 6)
v - (-5) = 30 - 10
v = 15 m/s

hence, final velocity = 15 m/s

Answer 2

Explanation:

The accleration time graph of particle moving with straight line. what isthe velocity of particle at t=8 sec if initial velocity of particle is 3 m/s