An object has a mass of 9 kg. The object's kinetic energy uniformly changes from 54 KJ to 45 KJ over t in [0, 4 s]. What is the average speed of the object?

1 Answer
Narad T.
Dec 2, 2017

The average speed is =104.8ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is m=9kg

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=54000J

The final kinetic energy is 1/2m u_2^2=45000J

Therefore,

u_1^2=2/9*54000=12000m^2s^-2

and,

u_2^2=2/9*45000=10000m^2s^-2

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

The points are (0,12000) and (4,10000)

The equation of the line is

v^2-12000=(10000-12000)/4t

v^2=-500t+12000

So,

v=sqrt(-500t+12000)

We need to calculate the average value of v over t in [0,4]

(4-0)bar v=int_0^4(sqrt(-500t+12000))dt

4 barv=[-500t+12000)^(3/2)/(3/2*-500))] _( 0) ^ (4)

=((-500*4+12000)^(3/2)/(-750))-((-500*0+12000)^(3/2)/(-750))

=12000^(3/2)/750-10000^(3/2)/750

=419.4

So,

barv=419.4/4=104.8ms^-1

The average speed is =104.8ms^-1

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