The first problem:

Originally Posted by **NSB3** A force increases linearly with time, F = c*t where c is a constant, and acts on an object of mass m. The object is at rest at t=0 and you have to calculate its velocity at a later time T. No other forces are acting on the object. No other information is given to you. Which of the following statements is true and describes a viable strategy to tackle this problem?
A. Energy for this system is conserved and you can easily calculate the final kinetic energy after first finding the potential energy that belongs to F.
B. The work-energy theorem is valid. You simply calculate the work done by F between t=0 and t=T to get the final kinetic energy.
C. You can use Newton's Second Law to calculate the acceleration a = F(t)/m. Then you integrate once with respect to time to obtain the final velocity.
D. Both B and C are valid strategies which are easily executed.
I thought it was A, is that correct? |

I am going to call "valid" strategies that can be performed without any heroic amounts of difficulty on an exam.

A is out: It is not obvious to me how to determine if a force is conservative if it is given as a function of time, not of position.

B is out: The work-energy theorem will, of course, work in any situation where there are no external (that is to say neglected) forces involved. However we have to calculate the work, which is found by Integral( F(t)dx ). It is not clear to me how to determine the x dependence of t without resorting to Newton's 2nd Law.

C is in: It is easy to calculate v as a function of t.

I would say the only valid strategy would be C. Though B and C certainly can both be done, B clearly gives difficultes.

-Dan