Question

(a) The velocity of a body moving in a straight line is increased by
applying a constant force F, for some distance in the direction of the
motion. Prove that the increase in the kinetic energy of the body is equal
to the work done by the force on the body.
(b) Calculate the velocity of a body of mass 8 kg If the Kinetic energy of
a body is 1600 J.​

Answer 1

We know that v

2

=u

2

+2as

And Work done =F×s for a constant force F.

Also we know that a =

m

F

​

v

2

−u

2

=2as

This gives s=

2a

v

2

−u

2

​

F=ma

We can write work done (W) by this force F as

W=ma(

2a

v

2

−u

2

​

)=

2

1

​

mv

2

−

2

1

​

mu

2

=(K.E)

f

​

−(K.E)

i

​

Hope this helps!

Answer 2

Explanation:

a) Using,

Work-Energy theorem

Work done by all = Change in kinetic energy

Thus,

Work done by force = Change in kinetic energy

b) 1/2 × 8 × v² = 1600 J

=> v² = 400 m²/s²

=> v = 20 m/s