An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 64 KJ to 160 KJ over t in [0, 12 s]. What is the average speed of the object?

1 Answer
Narad T.
Apr 24, 2017

The average speed is =234.8ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =4kg

The initial velocity is =u_1

1/2m u_1^2=64000J

The final velocity is =u_2

1/2m u_2^2=160000J

Therefore,

u_1^2=2/4*64000=32000m^2s^-2

and,

u_2^2=2/4*160000=80000m^2s^-2

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

The points are (0,32000) and (12,80000)

The equation of the line is

v^2-32000=(80000-32000)/12t

v^2=4000t+32000

So,

v=sqrt((4000t+32000)

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

(12-0)bar v=int_0^12sqrt((4000t+32000))dt

12 barv=[((4000t+32000)^(3/2)/(3/2*4000)]_0^12

=((4000*12+32000)^(3/2)/(6000))-((4000*0+32000)^(3/2)/(6000))

=80000^(3/2)/6000-32000^(3/2)/6000

=2817.2

So,

barv=2817.2/12=234.8ms^-1

Related questions
See all questions in Displacement and Velocity
Impact of this question
1368 views around the world
You can reuse this answer
Creative Commons License