Question

A body of mass 1 kg begins to move under the
action of a time dependent force F = (2ti +3t+j)N,
where i and į are unit vectors along x and y
axis. What power will be developed by the force at
the time t?
[NEET-2016]
(1) (28 + 31") W (2) (2x2 + 372) W
(3) (2 + 47) W (4) (2 + 3) W​

Answer 1

Answer:

A body mass 1 kg = 1000 and the 28+31= 59 w.and 2× 2×2=8+372w=380.

Answer 2

Dear student,

It given that a body of mass 1 kg begins to move under the action of time dependent force F = (2t i + 3t² j) N. We need find the power developed by the force at time t.

      ∵ P = F.v

To carry the solution further, we need to break the force into acceleration to obtain velocity. We know by formula that;

           F = ma

           a = F/m

           a =   (2t i + 3t² j)/ 1

           a =  (2t i + 3t² j) m/s²

    dv/dt =  (2t i + 3t² j)

         dv =  (2t i + 3t² j)dt

        ∫dv =  ∫(2dt² i + 3dt³ j)

        ∫dv = 2∫dt²i + 3∫dt³j

        ∫dv = ( t² i + t³ j ) m/s

Now putting the obtained values in (1), we get;

         P = F.v

         P =  ( t² i + t³ j ) (2t i + 3t² j)

        P = (2t³ + 3t⁵) W

Hence, the power developed by the force at time t will be  (2t³ + 3t⁵) W.