An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 104 KJ to 64KJ over t in [0,5s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 5, 2017

The average speed is =204.4ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =4kg

The initial velocity is =u_1

1/2m u_1^2=104000J

The final velocity is =u_2

1/2m u_2^2=64000J

Therefore,

u_1^2=2/4*104000=52000m^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 (0,52000) and (5,32000)

The equation of the line is

v^2-52000=(32000-52000)/5t

v^2=-4000t+52000

So,

v=sqrt((-4000t+52000)

We need to calculate the average value of v over t in [0,5]

(5-0)bar v=int_0^5sqrt((-4000t+52000))dt

5 barv=[((-4000t+52000)^(3/2)/(-3/2*4000)]_0^5

=((-4000*5+52000)^(3/2)/(-6000))-((-4000*0+52000)^(3/2)/(-6000))

=-32000^(3/2)/6000+52000^(3/2)/6000

=1022.2

So,

barv=1022.2/5=204.4ms^-1

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