Question

What happened to momentum if kinetic energy increase 3time?

Answer 1

Momentum becomes `(3)^(1/2)` times the initial momentum given that the Mass of the object is constant.

Explanation:

`KE_i = (1/2).m.v^2` and `vecP_i = mvecv`

`KE_f = 3KE_i = 3(1/2).m.v^2`

`rArr KE_f = (1/2).m.(v')^2` where `v' = (3)^(1/2)v`

`rArrvecP_f = mvecv' = m(3)^(1/2)vecv = (3)^(1/2)mvecv`

`:. vecP_f = (3)^(1/2)vecP_i`

Answer 2

`KE=1/2mv^2` and `P=m\Deltav`

Explanation:

So, if the kinetic energy increases 3 times (triples) that means that the velocity must have increased by `sqrt3`

If you start with mass m and velocity v , as noted above `KE=1/2mv^2`

So, if the velocity increased by a factor of `sqrt3`, the new velocity is `sqrt3v` and the new kinetic energy is `KE=1/2m(sqrt3v)^2`
which is `KE=1/2m*3*v^2->3KE=1/2mv^2`