Question

a body initially at rest is acted upon by a force F moves with an acceleration.a.for.time t show power spent on the body is 1/2aFt

Answer 1

Answer:

$\frac{Fv^{2} }{2a}$

Explanation:

Let us find the kinetic energy acting on the body. As it is given in the question that the body acquired a velocity v, the total energy of the body is equal to the kinetic energy of the body,

The kinetic energy of the body is equal to,

K.E=12mv2...(1)K.E=$\frac{1}{2}mv^{2}$...(1)

Also, the force acting on the body is equal to,

F=ma

⇒m=Fa...(2)

As the mass of the body is not given in the question, substitute equation 2 in equation 1, we greet,

K.E=$\frac{1}{2}$×$\frac{F}{a}$×$v^{2}$

⇒K.E=$\frac{Fv^{2} }{2a}$

As the work done by a body is equal to the change in kinetic energy of the body according to the work-energy theorem,

W=ΔK.E

W=$\frac{Fv^{2} }{2a}$

Hence, the above is the formula for work done in known terms.