An object has a mass of 4kg. The object's kinetic energy uniformly changes from 64KJ to 180KJ over t[0,12s]. What is the average speed of the object?

1 Answer
Jun 15, 2017

The average speed is =244.5ms1

Explanation:

The kinetic energy is

KE=12mv2

The mass is =4kg

The initial velocity is =u1

The initial kinetic energy is 12mu21=64000J

The final velocity is =u2

The final kinetic energy is 12mu22=180000J

Therefore,

u21=2464000=32000m2s2

and,

u22=24180000=90000m2s2

The graph of v2=f(t) is a straight line

The points are (0,32000) and (12,90000)

The equation of the line is

v232000=900003200012t

v2=4833.3t+32000

So,

v=(4833.3t+32000)

We need to calculate the average value of v over t[0,12]

(120)¯v=120(4833.3t+32000)dt

12¯v=(4833.3t+32000)32324833.3120

=(4833.312+32000)327250(4833.30+32000)327250

=9000032725032000327250

=2934.6

So,

¯v=2934.612=244.5ms1

The average speed is =244.5ms1