This is a 1-D problem. A force increases linearly with the x -coordinate, F = c

Question

This is a 1-D problem. A force increases linearly with the x-coordinate, F = c*x, where c is a constant, and acts on an object of mass m. The object starts from rest at x=0 and you have to calculate its velocity at later position x=A. No other forces are acting on the object. This is all the information given to you. Which of the following statement is true and describes a viable strategy to tackle this problem?

A. Energy is conserved. You can easily find the potential energy for F and calculate the final kinetic energy.

B. The work-energy theorem is valid. You integrate F with respect to x between 0 and A and thus obtain the kinetic energy at A.

C. Newton's Second Law gives you the acceleration as a=F(x)/m. Now it is very easy to integrate with respect to time to obtain the velocity.

D. Both A and B are correct and viable strategies

Explanation / Answer

B. The work-energy theorem is valid. You integrate F with respect to x between 0 and A and thus obtain the kinetic energy at A.

Th valid statement is B

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