An object has a mass of 12 kg. The object's kinetic energy uniformly changes from 81 KJ to 180 KJ over t in [0, 4 s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 22, 2017

The average speed is =146.6ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =12kg

The initial velocity is =u_1

1/2m u_1^2=81000J

The final velocity is =u_2

1/2m u_2^2=180000J

Therefore,

u_1^2=2/12*81000=13500m^2s^-2

and,

u_2^2=2/12*180000=30000m^2s^-2

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

The points are (0,13500) and (4,30000)

The equation of the line is

v^2-13500=(30000-13500)/4t

v^2=4125t+13500

So,

v=sqrt((4125t+13500)

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

(4-0)bar v=int_0^4sqrt((4125t+13500))dt

4 barv=[((4125t+13500)^(3/2)/(3/2*4125)]_0^4

=((4125*4+13500)^(3/2)/(6187.5))-((4125*0+13500)^(3/2)/(6187.5))

=30000^(3/2)/6187.5-13500^(3/2)/6187.5

=586.3

So,

barv=586.3/4=146.6ms^-1

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