Question

A time varying net force acting on a4.0kg particle causes the particle to have a displacement given by x=2.0t-3.0t2+1.0t3wher x in meters t in seconds

Answer 1

I assume the task is to find the force. Let $m=4kg$ be the mass of the particle. According to the second Newton's law, the net force on the particle is:

$$F =ma$$

where $a$ is the acceleration of the particle. By definition, the acceleration is the second derivative from the coordinate: $a(t) = x''(t)$ . Since the coordinate is given as follows:

$$x(t) = 2t-3t^2+t^3$$

obtain the acceleration:

$$a(t) = (2t-3t^2+t^3)'' = 6t-6$$

Thus, the force is:

$$F(t) = 4\cdot (6t-6)=24t-24\space\space (N)$$

Answer. $F(t)=24t-24\space\space (N)$