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

Answer:

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#