An object has a mass of 8 kg. The object's kinetic energy uniformly changes from 24 KJ to 42KJ over t in [0, 9 s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 21, 2017

The average speed is 90.5ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =8kg

The initial velocity is =u_1

1/2m u_1^2=24000J

The final velocity is =u_2

1/2m u_2^2=42000J

Therefore,

u_1^2=2/8*24000=6000m^2s^-2

and,

u_2^2=2/8*42000=10500m^2s^-2

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

The points are (0,6000) and (9,10500)

The equation of the line is

v^2-6000=(10500-6000)/9t

v^2=500t+6000

So,

v=sqrt((500t+6000)

We need to calculate the average value of v over t in [0,9]

(9-0)bar v=int_0^9sqrt((500t+6000))dt

9 barv=[((500t+6000)^(3/2)/(3/2*500)]_0^9

=((500*9+6000)^(3/2)/(750))-((500*0+6000)^(3/2)/(750))

=10500^(3/2)/750-6000^(3/2)/750

=814.9

So,

barv=814.9/9=90.5ms^-1

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