Power supplied to a particle of mass 2kg varies with time as P=3t^2 /2.Here t is in second.If velocity of the particle at t=0 is v=0.The velocity of particle at time t=2 sec will be?

  1. 1 m/s
  2. 2 m/s
  3. 4 m/s
  4. 2 #sqrt(2)# m/s

1 Answer
Feb 25, 2018

Power(#P#) = work done/time = #(dW)/(dt)#

So, #dW = Pdt#

given, #P=(3 t^2)/2#

so, #dW = 3/2 t^2 dt#

now, #int_0^W dW = 3/2 int_0^2 t^2dt#

so, #W = 1/2 [t^3]_0^2 = 4 J#

now, if the kinetic energy at time #t=2# was #1/2 mv^2#,where, #v# is the velocity at #t=2#

then, #1/2 mv^2 =4#

given, #m=2 Kg#, so #v=2 ms^-1#