A 2.2 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x = 3.0 m + (4.0 m/s)t + ct2 - (2.6 m/s3)t3, with x in meters and t in seconds. The factor c is a constant. At t = 3.0 s, the force on the particle has a magnitude of 36 N and is in the negative direction of the axis. What is c?
F = m*a
The Attempt at a Solution
I was given the hint: Acceleration is the second time derivative of the position function. The net force is related to the acceleration via Newton's second law.
I tried to take the 2nd derivative of the x equation, but I am not sure if I am doing it right because of all of the m's and m/s's, etc. along with the c and the t's.
I ended up getting 4+c*2t+t^2-7.8t^2 and then 2c-11.6t as my second derivative. (I had 2c-15.6t at first, but I think I had the product rule wrong in the first derivative then...)
I then solved a = 2c - 11.6(3) as 16.364 = 2c - 34.8, because 16.364 is the acceleration I found by dividing 36/2.2 (F/m). That solves for c as 25.58200. Apparently that is wrong, and I don't know why!