An object has a mass of 5 kg. The object's kinetic energy uniformly changes from 55 KJ to 24 KJ over t in [0,4s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 20, 2017

The average speed is =124.9ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =5kg

The initial velocity is =u_1

1/2m u_1^2=55000J

The final velocity is =u_2

1/2m u_2^2=24000J

Therefore,

u_1^2=2/5*55000=22000m^2s^-2

and,

u_2^2=2/5*24000=9600m^2s^-2

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

The points are (0,22000) and (4,9600)

The equation of the line is

v^2-22000=(9600-22000)/4t

v^2=-3100t+22000

So,

v=sqrt((-3100t+22000)

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

(4-0)bar v=int_0^4sqrt((-3100t+22000))dt

4 barv=[((-3100t+22000)^(3/2)/(-3/2*3100)]_0^4

=((-3100*4+22000)^(3/2)/(-4650))-((-3100*0+22000)^(3/2)/(-4650))

=22000^(3/2)/4650-9600^(3/2)/4650

=499.5

So,

barv=499.5/4=124.9ms^-1

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