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

Give an example also.

1 Answer
Aug 7, 2017

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