I have a trouble with this problem: Suppose you have a particle with mass 30Kg, this particle is in influence of a force F that acts along the x axis and F=6+4x-3(x^2) and at x=0 the particle has 0m/s speed. Find the total work made by F between x=0 and x=3, then find the power given to the particle when x=3. (answers= 9 Joules and 22 Watts) Well the first thing is easy, only I have to integrate F between 0 and 3. but the second question I can't see what's to be done. I try to use the fact that if I have the work I must get the final time but I don't have an expression for the trayectory. Another way I have tried is to get the function of position by the fact that F=ma, a=F/m dv/dt=(6+4x-3(x^2))/m this is a partial differential equation involving the second derivative of a function u(x,t) and the general solution I get is: u(x,t)=a(x)+b(x)t+(t^2)((6+4x-3(x^2))/2m) but I don't have the sufficient conditions to get a good boundary problem or initial problem to separate a particular solution. My questions are: what conditions could I put, or what other way, easier, could I take to solve this?