An object has a mass of `9 kg`. The object's kinetic energy uniformly changes from `135 KJ` to `45 KJ` over `t in [0, 4 s]`. What is the average speed of the object?

The given data:
Mass `m=9" "`kg
Kinetic Energy initial `KE_i=135000" "`joule
Kinetic Energy final `KE_f=45000" "`joule

initial time `t_0=0" "`sec
final time `t_1=4" "`sec

Compute for initial velocity `v_i`

`KE_i=1/2mv_i^2`

`135000=1/2(9)v_i^2`

`v_i^2=(2(135000))/9`

`v_i=sqrt(30000)`

`v_i=173.2050808" "`m/sec

Compute for final velocity `v_f`

`KE_f=1/2mv_f^2`

`45000=1/2(9)v_f^2`

`v_f^2=(2(45000))/9`

`v_f=sqrt(10000)`

`v_f=100" "`m/sec

Solve for the total distance traveled by the object using the following:

`v_f^2=v_i^2+2a*s" "`first equation
and
`v_f=v_i+a*t" "`second equation

`v_f^2-v_i^2=2a*s" "`from the first equation

`color(red)((v_f+v_i)(v_f-v_i)=2*a*s)`

`color(blue)((v_f-v_i)=a*t" ")`from the second equation

Divide the first equation by the second equation

`color(red)((v_f+v_i)cancel(v_f-v_i))/color(blue)(cancel(v_f-v_i))=color(red)(2*cancela*s)/color(blue)(cancela*t)`

`v_f+v_i=(2s)/t`

`s=1/2*t(v_f+v_i)`

`s=1/2*(4)(100+173.2050808)`

`s=546.4101616" "`m

Average speed `=("distance traveled")/("elapsed time")`

Average speed `=546.4101616/4`

Average speed `=136.6025404" "`m/sec

God bless....I hope the explanation is useful.