An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 42 KJ to 15 KJ over t in [0, 8 s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 6, 2017

The average speed is =96.5ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =6kg

The initial velocity is =u_1

1/2m u_1^2=42000J

The final velocity is =u_2

1/2m u_2^2=15000J

Therefore,

u_1^2=2/6*42000=14000m^2s^-2

and,

u_2^2=2/6*15000=5000m^2s^-2

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

The points are (0,14000) and (8,5000)

The equation of the line is

v^2-14000=(5000-14000)/8t

v^2=-1125t+14000

So,

v=sqrt((-1125t+14000)

We need to calculate the average value of v over t in [0,8]

(8-0)bar v=int_0^8sqrt((-1125t+14000))dt

8 barv=[((-1125t+14000)^(3/2)/(-3/2*1125)]_0^8

=((-1125*8+14000)^(3/2)/(-1687.5))-((-1125*0+14000)^(3/2)/(-1687.5))

=-5000^(3/2)/1685.5+14000^(3/2)/1687.5

=772.1

So,

barv=772.1/8=96.5ms^-1

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