An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #48 KJ# to # 320 KJ# over #t in [0, 12 s]#. What is the average speed of the object?

1 Answer
Jan 15, 2017

Answer:

Average speed is #227.46# #m/s#

Explanation:

Kinetic energy of an objeect of mass #m# kg. moving with a velocity of #v# #m/s# is given by #1/2mv^2# joules. Let the initial velocity is #u# and final velocity be #v#.

As the mass of the object is #4# #kg.# and initial kinetic energy is #48KJ# or #48000J#

We have #1/2xx4xxu^2=48000# i.e. #u^2=24000# and #u=sqrt24000=sqrt(40^2xx15)=40sqrt15=154.92# #m/s#

and as the mass of the object is #4# #kg.# and final kinetic energy is #320KJ# or #320000J#

#1/2xx4xxu^2=320000# i.e. #u^2=160000# and

#v=sqrt160000=400# #m/s#

Hence average speed is #(v+u)/2=(400+154.92)/2=554.92/2=227.46# #m/s#