An object has a mass of 5 kg. The object's kinetic energy uniformly changes from 15 KJ to 64KJ over t in [0,12s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 24, 2017

The average speed is =123.5ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =5kg

The initial velocity is =u_1

1/2m u_1^2=15000J

The final velocity is =u_2

1/2m u_2^2=64000J

Therefore,

u_1^2=2/5*15000=6000m^2s^-2

and,

u_2^2=2/5*64000=25600m^2s^-2

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

The points are (0,6000) and (12,25600)

The equation of the line is

v^2-6000=(25600-6000)/12t

v^2=1633.3t+6000

So,

v=sqrt((1633.3t+6000)

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

(12-0)bar v=int_0^12sqrt((1633.3t+6000))dt

12 barv=[((1633.3t+6000)^(3/2)/(3/2*1633.3)]_0^12

=((1633.3*12+6000)^(3/2)/(2450))-((1633.3*0+6000)^(3/2)/(2450))

=25600^(3/2)/2450-6000^(3/2)/2450

=1482.1

So,

barv=1482.1/12=123.5ms^-1

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