Question

A body of mass 5 kg initially at rest is moved by a horizontal force of 20 N on a frictionless
table. Calculate the work done by the force in 10 second and prove that this equals to the
change in kinetic energy.​

Answer 1

Given:-

Mass (m) = 5kg

Intial Velocity (u) = 0

Force (F) = 20N

Time (t) = 10s

To Find:-

(i)Work (W)

(ii)To prove Work = K.E

Formula:-

Work = Force × Displacement  ----(1)

Force = Mass × Acceleration------(2)

Final Velocity = Intial Velocity + Acceletation × Time------(3)

v² - u² = 2as-----(4)

Solution:-

Using formula 2 we have

20 = 5 × a

a = 20/5

a = 4 m/s²

Using Formula 3 we have

v = 0 + 4×10

v = 40 m/s

Using fourth formula we have,

(40)² - 0² = 2×4×s

1600 = 8s

s = 1600/8

s = 200m

Finally using formula 1, we have

Work = 20 × 200

Work =   4000 J OR 4 KJ

Now,

K.E = 1/2      mv²

= 1/2 × 5 × 1600

= 800 × 5

= 4000J OR 4KJ  = Work