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Question

If the KE of an arros is doubled, by what factor has its speed increased?
If its speed is doubled, by what factor does its KE increase?

Answer 1

K = (1/2) * m *v ^2

so v=SQRT[ 2*K/m ]

If K' = 2*K
then v'=SQRT[ 2*K'/m] ->
v'=SQRT[ 2*(2*K)/m] ->
v'=SQRT[ 2] * SQRT[2*K/m] ->
v'=SQRT[ 2] * v
So v'/v = SQRT[2]
The above analysis stands when mass remains unchanged and the change in kinetic energy K results from a change is velocity v (as we are lead to think from the phrasing of the question).

As for the second question:
K=(1/2)*m*v^2
and
K' = (1/2)*m*v' ^2 ->
K' = (1/2)*m*(2*v)^2 ->
K' = (1/2)*m*4*v^2 ->
K' = 4 * (1/2)*m*v^2 ->
K' = 4 K

Answer 2

What is an arros?

This is the formula for k-energy.

ke=1/2mv
m is the mass in kg
v is the velocity in meter per segond (m/s)

It the kinetic energy is 2x bigger and you want to find its speed (velocity or V)

ke/m=1/2v

If the velocity (v or speed) doubles then:
ke/m=2(1/2 v)
I know I know why double then divide by 2. Just to keep the habit of laying out the equations even simple ones, in case a mistake would slip in...

Now you know your formulas. You get a calculator and do your own math!!!
Good luck.

Answer 3

Kinetic energy of an object with a mass m, moving with velocity v equals:

K = m*v^2/2

So to double the Kinetic energy the speed must increase by a factor of sqrt(2) = 1.41.

If the speed is doubled, the kinetic energy is increased by a factor of 4.

Answer 4

KE varies as the square of the speed.
If the speed is doubled the KEwill be
quadrupled. or
KE will increase by a factor of 4