An object has a mass of 9 kg. The object's kinetic energy uniformly changes from 81 KJ to 18 KJ over t in [0, 4 s]. What is the average speed of the object?

1 Answer
Narad T.
Aug 30, 2017

The average speed is =103.0ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is =9kg

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=81000J

The final kinetic energy is 1/2m u_2^2=18000J

Therefore,

u_1^2=2/9*81000=18000m^2s^-2

and,

u_2^2=2/9*18000=4000m^2s^-2

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

The points are (0,18000) and (4,4000)

The equation of the line is

v^2-18000=(4000-18000)/4t

v^2=-3500t+18000

So,

v=sqrt((-3500t+18000)

We need to calculate the average value of v over t in [0,4]

(4-0)bar v=int_0^4(sqrt(-3500t+18000))dt

4 barv=[((-3500t+18000)^(3/2)/(-3/2*3500))]_0^4

=((-3500*4+18000)^(3/2)/(-5250))-((-3500*0+18000)^(3/2)/(-5250))

=18000^(3/2)/5250-4000^(3/2)/5250

=411.8

So,

barv=411.8/4=103.0ms^-1

The average speed is =103.0ms^-1

Related questions
See all questions in Displacement and Velocity
Impact of this question
1444 views around the world
You can reuse this answer
Creative Commons License