An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 120 KJ to 720 KJ over t in [0, 4 s]. What is the average speed of the object?

1 Answer
Narad T.
Jul 21, 2017

The average speed is =365.3ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is =6kg

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=720000J

Therefore,

u_1^2=2/6*120000=40000m^2s^-2

and,

u_2^2=2/6*720000=240000m^2s^-2

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

The points are (0,40000) and (4,240000)

The equation of the line is

v^2-40000=(240000-40000)/4t

v^2=50000t+40000

So,

v=sqrt((50000t+40000)

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

(4-0)bar v=int_0^4(sqrt(50000t+40000))dt

4 barv=[((50000t+40000)^(3/2)/(3/2*50000))]_0^4

=((50000*4+40000)^(3/2)/(75000))-((50000*0+40000)^(3/2)/(75000))

=240000^(3/2)/75000-40000^(3/2)/75000

=1461

So,

barv=1461/4=365.3ms^-1

The average speed is =365.3ms^-1

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