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

Answer is 15 m/s .Integrate 2t-2 and apply limit from 0 to v for velocity since the body starts from rest and 0 to 5 for the time. You will get your answer

We know, A=dv/dtdv=AdtPutting the value of A in the above equation, and integrating `v` from 0 to v` since we require v` here.And integrating time from 0 to 5 s.Solving, we get: v`=t^2-

They have given acceleration,and asked to find velocity at 5s,then we should integrate acceleration then we get t^2.t=5 then v=5×5=25m/s

As we know that change in velocity divided by change in time is the acceleration, we can writedv/dt = adv = a dtNow integrate both the sides. Limit the velocity from 0 to v. Limit the time from 0 to 5.dv = 2 (t-1) dtAfter integration:V = t^2 - 2t.Now using the limits, v = 5^2 - 2 (5)V = 25 - 10 = 15.Hence the answer is 15m/s.

Integrate 2t-2 with respect to t , you will get it as ( t^2-2t ) then put the value of t and hence answer is 15.