An object has a mass of #5 kg#. The object's kinetic energy uniformly changes from #150 KJ# to # 42KJ# over #t in [0,8s]#. What is the average speed of the object?

1 Answer
Narad T.
Nov 12, 2016

The average speed is #=142.5 ms^(-1)#

Explanation:

The kinetic energy #=(mv^2)/2#
Let #u_0# be the initial velocity and
#u_1# the final velocity.
The average speed is #=(u_0+u_1)/2#

#m*u_0^2/2=150*10^3#
#:. u_0^2=150*10^3/5# #=>##u_0=sqrt(30*10^3)=173.2 ms^(-1)#

#m*u_1^2/2=42*10^3#
#:. u_1^2=42*10^3/5# #=>##u_1=sqrt(42*200)=91.7 ms^(-1)#

The average speed is #(173.2+91.7)/2=142.5 ms^(-1)#

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