An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 16 KJ to 66KJ over t in [0, 6 s]. What is the average speed of the object?

1 Answer
Narad T.
Jun 15, 2018

The average speed is =140.8ms^-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=16000J

The final kinetic energy is 1/2m u_2^2=66000J

Therefore,

u_1^2=2/4*16000=8000m^2s^-2

and,

u_2^2=2/4*66000=33000m^2s^-2

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

The points are (0,8000) and (6, 33000)

The equation of the line is

v^2-8000=(33000-8000)/6t

v^2=4166.7t+8000

So,

v=sqrt(4166.7t+8000)

We need to calculate the average value of v over t in [0,6]

(6-0)bar v=int_0^6(sqrt(4166.7t+8000))dt

6 barv= [(4166.7t+8000)^(3/2)/(3/2*4166.7)] _( 0) ^ (6)

=((4166.7*6+8000)^(3/2)/(6250))-((4166.7*0+8000)^(3/2)/(6250))

=33000^(3/2)/6250-8000^(3/2)/6250

=844.67

So,

barv=844.67/6=140.8ms^-1

The average speed is =140.8ms^-1

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