An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 12 KJ to 360 KJ over t in [0, 12 s]. What is the average speed of the object?

1 Answer
Narad T.
Aug 17, 2017

The average speed is =290.8ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is =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=12000J

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

Therefore,

u_1^2=2/4*12000=6000m^2s^-2

and,

u_2^2=2/4*360000=180000m^2s^-2

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

The points are (0,6000) and (12,180000)

The equation of the line is

v^2-6000=(180000-6000)/12t

v^2=14500t+6000

So,

v=sqrt((14500t+6000)

We need to calculate the average value of v over t in [0,12]

(12-0)bar v=int_0^12(sqrt(14500t+6000))dt

12 barv=[((14500t+6000)^(3/2)/(3/2*14500))]_0^12

=((14500*12+6000)^(3/2)/(21750))-((14500*0+6000)^(3/2)/(21750))

=180000^(3/2)/21750-6000^(3/2)/21750

=3489.8

So,

barv=3489.8/12=290.8ms^-1

The average speed is =290.8ms^-1

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