What happens to the kinetic energy of an object if we halve the velocity?

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Answer 1 · 2017-12-16T17:15:10

See below.

Kinetic energy is given by #K=1/2mv^2#

where #m# is the mass of the object, and #v# is the object's velocity (speed).

If we halve the object's velocity, we're saying that the final velocity is #1/2# the initial velocity, or in symbolic terms, #v_f=1/2v_i#.

So, initially we would have #K_i=1/2mv_i^2# and finally we would have:

#K_f=1/2mv_f^2#

#=1/2m*(1/2v_i)^2#

Note that the entire quantity—including both the #1/2# and #v# term—is squared.

#=>1/2m*1/4v_i^2#

Rearranging:

#=>1/4(1/2mv_i^2)#

#=1/4K_i#

#:.# We can see that the final kinetic energy of the object is #1/4# of the kinetic energy initially possessed by the object.