Kinetic Energy Calculation Using Average Velocity

[renob]

I need to find kinetic energy, but I am given several velocities over 4 seconds. Would it be correct if I use the average velocity to calculate the KE?

question:

A force acts on a 3.0 kg particle-like object in such a way that the position of the object as a function of time is given by x=3.0t-4.0t^2+1.0t^3, with x in meters and t in seconds. Find the work done on the object by the force from t=0 to t= 4.0s.

 

[Delphi51]

More information needed!
Does the same object have a velocity that varies with time?
If so, your KE also varies with time and perhaps you should report the several values for KE. If you must average, better to average the KE's rather than the velocities.

 

[renob]

Yea the velocity changes with time. So average the KE's?

 

[Delphi51]

Yikes, that x=3.0t-4.0t^2+1.0t^3 is more additional information that I wanted to see!
Looks like acceleration varying with time. One approach would be to figure out the velocity function, then evaluate it at time 0 and time 4. Then you can find the KE at the beginning and the KE at the end. The difference should be the work done.

Is this question from a calculus class? If so, you could differentiate the x function to get the velocity and acceleration. Then integrate dW = Fdx to get the work done.

 

[renob]

Nah it's from ap physics which is calculus based. Thanks for the advice.

 

[Delphi51]

It works out quite easily both ways - I even got the same answer both ways. About 175*m.