Question

Can velocity and K.E doubled at the same time?

Give an example also.

Answer 1

See below.

Explanation:

In a mechanical conservative system we have

`1/2m v_1^2+mgh_1 = E`

The new condition is

`m v_1^2+mg h_2 = E`

now subtracting term to term

`1/2mv_1^2+mg(h_2-h_1)=0` or

`1/2v_1^2=g(h_1-h_2)` considering now a time interval `Delta t` and choosing `v_1 = (h_1-h_2)/(Deltat)` we have

`1/2v_1^2=g v_1 Delta t` or

`v_1/(Delta t) = 2g`

So to move from the initial configuration to the second is necessary an elapsed time `Delta t` so it can't be done at the same time. And the change must be executed with an acceleration

`a approx v_1/(Delta t) = 2g`