An object has a mass of 2 kg. The object's kinetic energy uniformly changes from 35 KJ to 18 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 =162.1ms^-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=35000J

The final kinetic energy is 1/2m u_2^2=18000J

Therefore,

u_1^2=2/2*35000=35000m^2s^-2

and,

u_2^2=2/2*18000=18000m^2s^-2

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

The points are (0,35000) and (15,18000)

The equation of the line is

v^2-35000=(18000-35000)/15t

v^2=-1133.3t+35000

So,

v=sqrt(-1133.3t+35000)

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

(15-0)bar v=int_0^15(sqrt(-1133.3t+35000))dt

15 barv= (-1133.3t+35000)^(3/2)/(3/2*-1133.3)| _( 0) ^ (15)

=((-1133.3*15+35000)^(3/2)/(-1700))-((-1133.3*0+35000)^(3/2)/(-1700))

=35000^(3/2)/1700-18000^(3/2)/1700

=2431.1

So,

barv=2431.1/15=162.1ms^-1

The average speed is =162.1ms^-1

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