Question

Calculate the decrease in the kinetic energy of a moving body if its velocity reduces to half of the initial velocity.

Answer 1

We know for kinetic energy, body must have velocity
Let initial velocity = v
Also, Kinetic energy is equal to

K.E. = `1/2"m""v"^2`

given velocity decreased to half, so new velocity v'

v' = `"v"/2`

= K.E_new = `1/2 "m" xx ("v"/2)2`

= K.E_new = `1/2 "m" "v"^2/4`

∴ K.E_new = `("m""v"^2)/8`

Now, as asked, we need to find the decrease

Δ K.E = `("m""v"^2)/2 - ("m""v"^2)/8`

Δ K.E = `3/4"m""v"^2`

Kinetic energy will decrease by `3/4`th of initial kinetic energy.