An object has a mass of 12 kg. The object's kinetic energy uniformly changes from 254 KJ to 24 KJ over t in [0, 5 s]. What is the average speed of the object?

1 Answer
Narad T.
Jan 9, 2018

The average speed is =147.1ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is m=12kg

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=254000J

The final kinetic energy is 1/2m u_2^2=24000J

Therefore,

u_1^2=2/12*254000=42333.3m^2s^-2

and,

u_2^2=2/12*24000=4000m^2s^-2

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

The points are (0,42333.3) and (5,4000)

The equation of the line is

v^2-42333.3=(4000-42333.3)/5t

v^2=-7666.7t+42333.3

So,

v=sqrt(-7666.7t+42333.3)

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

(5-0)bar v=int_0^5(sqrt(-7666.7t+42333.3))dt

5 barv= (-7666.7t+42333.3)^(3/2)/(3/2*-7666.7)| _( 0) ^ (5)

=((-7666.7*5+42333.3)^(3/2)/(-11500))-((-7666.7*0+42333.3)^(3/2)/(-11500))

=42333.3^(3/2)/11500-4000^(3/2)/11500

=735.4

So,

barv=735.4/5=147.1ms^-1

The average speed is =147.1ms^-1

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