An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 84 KJ to 124KJ over t in [0, 6 s]. What is the average speed of the object?

1 Answer
Narad T.
Mar 27, 2017

The average speed is =227.7ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =4kg

The initial velocity is =u_1

1/2m u_1^2=84000J

The final velocity is =u_2

1/2m u_2^2=124000J

Therefore,

u_1^2=2/4*84000=42000m^2s^-2

and,

u_2^2=2/4*124000=62000m^2s^-2

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

The points are (0,42000) and (6,62000)

The equation of the line is

v^2-42000=(62000-42000)/6t

v^2=3333.3t+42000

So,

v=sqrt((3333.3t+42000)

We need to calculate the average value of v over t in [0,6]

(6-0)bar v=int_0^6sqrt((3333.3t+42000)dt

6 barv=[((3333.3t+42000)^(3/2)/(3/2*3333.3)]_0^3

=((3333.3*6+42000)^(3/2)/(5000))-((3333.3*0+42000)^(3/2)/(5000))

=62000^(3/2)/5000-42000^(3/2)/5000

=1366.1

So,

barv=1366.1/6=227.7ms^-1

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