An object has a mass of 9 kg. The object's kinetic energy uniformly changes from 99 KJ to 45 KJ over t in [0, 4 s]. What is the average speed of the object?

1 Answer
Narad T.
May 3, 2017

The average speed is =125.7ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =9kg

The initial velocity is =u_1

1/2m u_1^2=99000J

The final velocity is =u_2

1/2m u_2^2=45000J

Therefore,

u_1^2=2/9*99000=22000m^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 (0,22000) and (4,10000)

The equation of the line is

v^2-22000=(10000-22000)/4t

v^2=-3000t+22000

So,

v=sqrt((-3000t+22000)

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

(4-0)bar v=int_0^4sqrt((-3000t+22000))dt

4 barv=[((-3000t+22000)^(3/2)/(-3/2*3000)]_0^4

=((-3000*4+22000)^(3/2)/(-4500))-((-3000*0+22000)^(3/2)/(-4500))

=22000^(3/2)/4500-10000^(3/2)/4500

=502.9

So,

barv=502.9/4=125.7ms^-1

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