An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 66 KJ to 225 KJ over t in [0, 8 s]. What is the average speed of the object?

1 Answer
Narad T.
Jul 13, 2017

The average speed is =217.3ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

The mass is =6kg

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=66000J

The final kinetic energy is 1/2m u_2^2=225000J

Therefore,

u_1^2=2/6*66000=22000m^2s^-2

and,

u_2^2=2/6*225000=75000m^2s^-2

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

The points are (0,22000) and (8,75000)

The equation of the line is

v^2-22000=(75000-22000)/8t

v^2=6625t+22000

So,

v=sqrt((6625t+22000)

We need to calculate the average value of v over t in [0,8]

(8-0)bar v=int_0^8sqrt(6625t+22000))dt

8 barv=[((6625t+22000)^(3/2)/(3/2*6625)]_0^8

=((6625*8+22000)^(3/2)/(9937.5))-((6625*0+22000)^(3/2)/(9937.5))

=75000^(3/2)/9937.5-22000^(3/2)/9937.5

=1738.5

So,

barv=1738.5/8=217.3ms^-1

The average speed is =217.3ms^-1

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