Question

A 1 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x = 1 m + (3 m/s)t + ct2 - (2 m/s3)t3 with x in meters and t in seconds.The factor c is a constant. At t = 3 s the force on the particle has a magnitude of 31 N and is in the negative direction of the axis. What is c?

Answer 1

X=1+3t+ct^2-2t^3
Differentiating the expression with respect to time
V=3+2ct-6t^2
Again differentiating with respect to time
a=2c-12t

Answer 2

Force=mass × acceleration
F=1(2c-12t)

At t=3 sec F=31N
31=2c-12(3)