An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 84 KJ to 96KJ over t in [0, 6 s]. What is the average speed of the object?

1 Answer
Narad T.
Oct 29, 2017

The average speed is =212.1ms^-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=84000J

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

Therefore,

u_1^2=2/4*84000=42000m^2s^-2

and,

u_2^2=2/4*96000=48000m^2s^-2

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

The points are (0,42000) and (6,48000)

The equation of the line is

v^2-42000=(48000-42000)/6t

v^2=1000t+42000

So,

v=sqrt((1000t+42000)

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

(16-0)bar v=int_0^6(sqrt(1000t+42000))dt

6 barv=[((1000t+42000)^(3/2)/(3/2*1000))]_0^6

=((1000*6+42000)^(3/2)/(1500))-((1000*0+42000)^(3/2)/(1500))

=48000^(3/2)/1500-42000^(3/2)/1500

=1272.6

So,

barv=1272.6/6=212.1ms^-1

The average speed is =212.1ms^-1

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