An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 18 KJ to 4KJ over t in [0, 9 s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 4, 2017

The average speed of the object is =72.8ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =4kg

The initial velocity is =u_1

1/2m u_1^2=18000J

The final velocity is =u_2

1/2m u_2^2=4000J

Therefore,

u_1^2=2/4*18000=9000m^2s^-2

and,

u_2^2=2/4*4000=2000m^2s^-2

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

The points are (0,9000) and (9,2000)

The equation of the line is

v^2-9000=(2000-9000)/9t

v^2=-777.8t+9000

So,

v=sqrt((-777.8t+9000)

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

(9-0)bar v=int_0^9sqrt((-777.8t+9000))dt

9 barv=[((-777.8t+9000)^(3/2)/(-3/2*777.8)]_0^9

=((-777.8*9+9000)^(3/2)/(-1166.7))-((-777.8*0+9000)^(3/2)/(-1166.7))

=-2000^(3/2)/1166.7+9000^(3/2)/1166.7

=655.2

So,

barv=655.2/9=72.8ms^-1

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