An object has a mass of 2 kg. The object's kinetic energy uniformly changes from 16 KJ to 96 KJ over t in [0, 15 s]. What is the average speed of the object?

1 Answer
Narad T.
Jan 13, 2018

The average speed is =231.0ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is m=2kg

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=16000J

The final kinetic energy is 1/2m u_2^2=96000J

Therefore,

u_1^2=2/2*16000=16000m^2s^-2

and,

u_2^2=2/2*96000=96000m^2s^-2

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

The points are (0,16000) and (15,96000)

The equation of the line is

v^2-16000=(96000-16000)/15t

v^2=5333.3t+16000

So,

v=sqrt(5333.3t+16000)

We need to calculate the average value of v over t in [0,15]

(15-0)bar v=int_0^15(sqrt(5333.3t+16000))dt

15 barv= (5333.3t+16000)^(3/2)/(3/2*5333.3)| _( 0) ^ (15)

=((5333.3*15+16000)^(3/2)/(8000))-((5333.3*0+16000)^(3/2)/(8000))

=96000^(3/2)/8000-16000^(3/2)/8000

=3465.1

So,

barv=3465.1/15=231.0ms^-1

The average speed is =231.0ms^-1

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