An object has a mass of 3 kg. The object's kinetic energy uniformly changes from 75 KJ to 45 KJ over t in [0, 9 s]. What is the average speed of the object?

1 Answer
Narad T.
Jun 26, 2017

The average speed is =199.5ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is =3kg

The initial velocity is =u_1ms^-1

The final velocity is =u_2 ms^-1

The initial kinetic energy is 1/2m u_1^2=75000J

The final kinetic energy is 1/2m u_2^2=45000J

Therefore,

u_1^2=2/3*75000=50000m^2s^-2

and,

u_2^2=2/3*45000=30000m^2s^-2

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

The points are (0,50000) and (9,30000)

The equation of the line is

v^2-50000=(30000-50000)/9t

v^2=-2222.2t+50000

So,

v=sqrt((-2222.2t+50000)

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

(9-0)bar v=int_0^3sqrt(-2222.2t+50000))dt

9 barv=[((-2222.2t+50000)^(3/2)/(-3/2*2222.2)]_0^9

=((-2222.2*9+50000)^(3/2)/(-3333.3))-((-2222.2*0+50000)^(3/2)/(-3333.3))

=50000^(3/2)/3333.3-30000^(3/2)/3333.3

=1795.3

So,

barv=1795.3/9=199.5ms^-1

The average speed is =199.5ms^-1

Related questions
See all questions in Displacement and Velocity
Impact of this question
1482 views around the world
You can reuse this answer
Creative Commons License