An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 640 KJ to 320 KJ over t in [0, 12 s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 4, 2017

The average velocity is =487.6ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =4kg

The initial velocity is =u_1

1/2m u_1^2=640000J

The final velocity is =u_2

1/2m u_2^2=320000J

Therefore,

u_1^2=2/4*640000=320000m^2s^-2

and,

u_2^2=2/4*320000=160000m^2s^-2

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

The points are (0,320000) and (12,160000)

The equation of the line is

v^2-320000=(160000-320000)/12t

v^2=-13333.3t+320000

So,

v=sqrt((-13333.3t+320000)

We need to calculate the average value of v over t in [0,12]

(12-0)bar v=int_0^12sqrt((-13333.3t+320000))dt

12 barv=[((-13333.3t+320000)^(3/2)/(-3/2*13333.3)]_0^12

=((-13333.3*12+320000)^(3/2)/(-20000))-((-13333.3*0+320000)^(3/2)/(-20000))

=-160000^(3/2)/20000+320000^(3/2)/20000

=5851

So,

barv=5851/12=487.6ms^-1

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