An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 128 KJ to 32 KJ over t in [0, 5 s]. What is the average speed of the object?

1 Answer
Narad T.
Jan 11, 2018

The average speed is =196.8ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is m=4kg

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=128000J

The final kinetic energy is 1/2m u_2^2=32000J

Therefore,

u_1^2=2/4*128000=64000m^2s^-2

and,

u_2^2=2/4*32000=16000m^2s^-2

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

The points are (0,64000) and (5,16000)

The equation of the line is

v^2-64000=(16000-64000)/5t

v^2=-9600t+64000

So,

v=sqrt(-9600t+64000)

We need to calculate the average value of v over t in [0,5]

(5-0)bar v=int_0^5(sqrt(-9600t+64000))dt

5 barv= (-9600t+64000)^(3/2)/(3/2*-9600)| _( 0) ^ (5)

=((-9600*5+64000)^(3/2)/(-14400))-((-9600*0+64000)^(3/2)/(-14400))

=64000^(3/2)/14400-16000^(3/2)/14400

=983.82

So,

barv=983.82/5=196.8ms^-1

The average speed is =196.8ms^-1

Related questions
See all questions in Displacement and Velocity
Impact of this question
1396 views around the world
You can reuse this answer
Creative Commons License