Mathematics Problem Of the Week

Spring 2006

POW #9

Particle in Motion

A particle of unit mass moves in one dimension under the action of a force that is a function, f(v), of its velocity, v. After observing the motion, the position at any time t is found to follow the cubic function x(t)=at+bt²+ct³, where a, b, and c are real numbers. Use this information to find a formula for f(v) as a function of v and the coefficients (but not t).

Hint: Since the particle has unit mass, the famous equation F=ma says that f(v) is the acceleration.

Note: You can get partial credit for solving for special cases of the coefficients a, b and c.

Due Friday, April 7^th Noon

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.