An object has a mass of 2 kg. The object's kinetic energy uniformly changes from 75 KJ to 42 KJ over t in [0, 15 s]. What is the average speed of the object?

1 Answer
Narad T.
Nov 13, 2017

The average speed is =241.1ms^-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=75000J

The final kinetic energy is 1/2m u_2^2=42000J

Therefore,

u_1^2=2/2*75000=75000m^2s^-2

and,

u_2^2=2/2*42000=42000m^2s^-2

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

The points are (0,75000) and (15,42000)

The equation of the line is

v^2-75000=(42000-75000)/15t

v^2=-2200t+75000

So,

v=sqrt(-2200t+75000)

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

(15-0)bar v=int_0^15(sqrt(-2200t+75000))dt

15 barv=[((-2200t+75000)^(3/2)/(-3/2*2200))]_0^15

=((-2200*15+75000)^(3/2)/(-3300))-((-2200*0+75000)^(3/2)/(-3300))

=75000^(3/2)/3300-42000^(3/2)/3300

=3615.8

So,

barv=3615.8/15=241.1ms^-1

The average speed is =241.1ms^-1

Related questions
See all questions in Displacement and Velocity
Impact of this question
1440 views around the world
You can reuse this answer
Creative Commons License