Question

Starting from the rest the acceleration of a particle is a=2(t-1). the velocity of the particle at t=5s is?

Answer 1

I'm getting 15m/s as the velocity.

Answer 2

If you know the basics of kinematics then you know that area under acceleration-time graph gives velocity.
Now, since equation is given ,instead of drawing graph we'll simply integrate the equation with respect to dt.

And taking upper limit t = 5s and lower limit t = 0s. Assuming body is at rest at t = 0s.

After integration equation becomes

v = t^2 - 2t [with limits 5 and 0]

Applying limits we get..

v = 15m/s