An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 16 KJ to 96KJ over t in [0, 6 s]. What is the average speed of the object?

1 Answer
Apr 27, 2017

163.345

Explanation:

Here, let's assume that uniform change means that the graph of Kinetic energy vs. time is a straight line.

Let y coordinate be kinetic energy, and x coordinate be time. As at x=0, y=16000, so y-intercept of line is 16000.

Slope of the line is (96000-16000)/(6-0)=40000/3

Equation of line is
y = (40000/3)x + 16000

K.E. = (40000/3)t + 16000

1/2 mv^2 = (40000/3)t + 16000
Putting value of m as 4 and simplifying:

v^2 = (20000/3)t + 8000
v = sqrt((20000/3)t + 8000)

Putting v=(ds)/dt, taking dt to R.H.S and integrating from t=0 to t=6, we get

s = int_0^6(sqrt((20000/3)t + 8000))dt

Upon integrating (which I leave up to you), s~~980.07

We know that average speed = total distance / total time.

So Avg. Speed ~~980.07/6

Avg. Speed ~~163.345 m/s