An object has a mass of 4kg. The object's kinetic energy uniformly changes from 144KJ to 120KJ over t[0,2s]. What is the average speed of the object?

1 Answer
Aug 14, 2017

The average speed is =256.8ms1

Explanation:

The kinetic energy is

KE=12mv2

The mass is =4kg

The initial velocity is =u1ms1

The final velocity is =u2ms1

The initial kinetic energy is 12mu21=144000J

The final kinetic energy is 12mu22=120000J

Therefore,

u21=24144000=72000m2s2

and,

u22=24120000=60000m2s2

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

The points are (0,72000) and (2,60000)

The equation of the line is

v272000=60000720002t

v2=6000t+72000

So,

v=(6000t+72000)

We need to calculate the average value of v over t[0,2]

(20)¯v=20(6000t+72000)dt

2¯v=(6000t+72000)3232600020

=(60002+72000)329000(60000+72000)329000

=7200032900060000329000

=513.6

So,

¯v=513.62=256.8ms1

The average speed is =256.8ms1