An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 630 KJ to 360 KJ over t in [0, 4 s]. What is the average speed of the object?

1 Answer
Narad T.
Jan 18, 2018

The average speed is =404.9ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is m=6kg

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=630000J

The final kinetic energy is 1/2m u_2^2=360000J

Therefore,

u_1^2=2/6*630000=210000m^2s^-2

and,

u_2^2=2/6*360000=120000m^2s^-2

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

The points are (0,210000) and (4,120000)

The equation of the line is

v^2-210000=(120000-210000)/4t

v^2=-22500t+210000

So,

v=sqrt(-22500t+210000)

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

(4-0)bar v=int_0^4(sqrt(-22500t+210000))dt

4 barv= (-22500t+210000)^(3/2)/(3/2*-22500)| _( 0) ^ (4)

=((-22500*4+210000)^(3/2)/(-33750))-((-22500*0+210000)^(3/2)/(-33750))

=210000^(3/2)/33750-120000^(3/2)/33750

=1619.7

So,

barv=1619.7/4=404.9ms^-1

The average speed is =404.9ms^-1

Related questions
See all questions in Displacement and Velocity
Impact of this question
1685 views around the world
You can reuse this answer
Creative Commons License