An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 0 KJ to 96KJ over t in [0, 6 s]. What is the average speed of the object?

1 Answer
Narad T.
Feb 1, 2018

The average speed is =9.94ms^-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=0J

The final kinetic energy is 1/2m u_2^2=96000J

Therefore,

u_1^2=2/4*0=0m^2s^-2

and,

u_2^2=2/4*96000=48000m^2s^-2

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

The points are (0,0) and (6,48000)

The equation of the line is

v^2=(48000-0)/6t

v^2=8000t

So,

v=sqrt(8000t)

We need to calculate the average value of v over t in [0,6]

(6-0)bar v=int_0^6(sqrt(8000t))dt

6 barv= [(8000t)^(3/2)/(3/2*8000)] _( 0) ^ (6)

=((8000*6)^(3/2)/(12000))-((8000*0)^(3/2)/(12000))

=8000^(3/2)/12000

=59.63

So,

barv=58.63/6=9.94ms^-1

The average speed is =9.94ms^-1

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