On a stationary block of mass 2 kg, a horizontal force F starts acting at t = 0 whose variation with time is shown in figure. Coefficient of friction between the block and ground is 0.5. Now answer the following questions:Find the time when acceleration of the block is zero.Find the velocity of the block when for the first time its acceleration becomes zero.Find the velocity of the block at t = 12 s.

fl=fk=0.5×2g=10NInitiallyF=20N>fl, so the block will start accelerating immediately. At any time t:F=20−2t Acceleration: a=20−2t−fkm=10−2tm    ……….(i) For a=0,10−2t2=0⇒t=5s  ………(ii) From Eq. (i), dvdt=10−2t2=5−t∫0v dv=∫0t (5−t)dt ⇒ v=5t−t22Let us see when the velocity becomes zero. For this:5t−t22=0⇒t=10sWe see that at t = 10 s, also F = 0. So the block has no tendency to move. Hence, acceleration is zero at this time. Now the block will not move from t = 10 s to 15 s, because for this magnitude of F < 10N. So block will remain at rest from t = 10 s to 15 s or acceleration is zero from 10 to 15 s.From Eq. (1), first time acceleration, becomes zero at t=5 s.Velocity at this timev=5t−t22=5×5−522=12.5ms−1From the above discussion, clearly, velocity is zero at t = 12 s.