An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 120 KJ to 64KJ over t in [0,8s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 8, 2018

The average speed is =213.6ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is m=4kg

The initial velocity is =u_1ms^-1

The final velocity is =u_2 ms^-1

The initial kinetic energy is 1/2m u_1^2=120000J

The final kinetic energy is 1/2m u_2^2=64000J

Therefore,

u_1^2=2/4*120000=60000m^2s^-2

and,

u_2^2=2/4*64000=32000m^2s^-2

The graph of v^2=f(t) is a straight line

The points are (0,60000) and (8,32000)

The equation of the line is

v^2-60000=(32000-60000)/8t

v^2=-3500t+60000

So,

v=sqrt(-3500t+60000)

We need to calculate the average value of v over t in [0,8]

(8-0)bar v=int_0^8(sqrt(-3500t+60000))dt

8 barv= [(-3500t+60000)^(3/2)/(3/2*-3500)] _( 0) ^ (8)

=((-3500*8+60000)^(3/2)/(-5250))-((-3500*0+60000)^(3/2)/(-5250))

=60000^(3/2)/5250-32000^(3/2)/5250

=1709.1

So,

barv=1709.1/8=213.6ms^-1

The average speed is =213.6ms^-1

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