An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #96 KJ# to # 280 KJ# over #t in [0, 12 s]#. What is the average speed of the object?

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Answer 1 · 2017-02-16T12:40:25

The average speed is #=296.65ms^-1#

The initial kinetic energy is #=1/2m u^2#

So,

#1/2m u^2=96000#

#u^2=2*96000/4=48000#

#v=sqrt48000=219.1ms^-1#

The final kinetic energy is #1/2m v^2#

So,

#1/2m v^2=280000#

#v^2=2*280000/4=140000#

#v=sqrt140000=374.2ms^-1#

On a graph velocity v/s time, we have a straight line #DC#

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#AD=u#

#BC=v#

#AB=t#

Area of #ABCD=(AD+BC)/2*t#

The average speed #=barv#

#barv*t=(AD+BC)/2*t#

so,

#barv=(u+v)/2#

#=(219.1+374.2)/2#

#=296.65ms^-1#