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

It is known that,

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

So,

$\frac{dv}{dt} = 2(t-1)$
$\int_0^v dv= \int _0^52(t-1)dt$
$=[t^2-2t]_0^5$
= (25 - 10) - (0)
= 15 m/s

Hence the velocity of partice at t = 5 sec is 15 m/s

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