Energy of an object

Question

If the kinetic energy of an object is tripled, by what factor is its speed
increased?

 

b) if the speed of an object is reduced to ¼ its original value, by what
factor does the kinetic energy change?

Answer 1

I like to use primes to indicate changed variables.

 

 

K´= 3K and m' = m by assumption, then K' = (1/2)m'v'² = (1/2)mv'² = 3(1/2)mv².

 

Cancelling 1/2 and m, we get v'² = 3v²  or  v' = √3 v.

 

 

v' = (1/4) v = v/4

 

K' = (1/2)mv'² = (1/2)m(v/4)² = (1/2)mv²/16 = K/16

 

The kinetic energy is reduced by a factor of 16.