An object has a mass of 5 kg. The object's kinetic energy uniformly changes from 150 KJ to 16KJ over t in [0,8s]. What is the average speed of the object?

1 Answer
Narad T.
Jun 5, 2017

The average speed is =176.4ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is =5kg

The initial velocity is =u_1

The initial kinetic energy is 1/2m u_1^2=150000J

The final velocity is =u_2

The final kinetic energy is 1/2m u_2^2=16000J

Therefore,

u_1^2=2/5*150000=60000m^2s^-2

and,

u_2^2=2/5*16000=6400m^2s^-2

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

The points are (0,60000) and (8,6400)

The equation of the line is

v^2-60000=(6400-60000)/8t

v^2=-6700t+60000

So,

v=sqrt((-6700t+60000)

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

(8-0)bar v=int_0^8sqrt((-6700t+60000))dt

8 barv=[((-6700t+60000)^(3/2)/(-3/2*6700)]_0^8

=((-6700*8+60000)^(3/2)/(-10050))-((-6700*0+60000)^(3/2)/(-10050))

=60000^(3/2)/10050-6400^(3/2)/10050

=1411.4

So,

barv=1411.4/8=176.4ms^-1

The average speed is =176.4ms^-1

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