Finding Kinetic Energy, Acceleration Magnitude

Question

I have this huge test coming up in a few days and there were some practice questions that we were given and I worked out the rest but this question has me completely clueless and lost...

A 5.60-kg particle moves along the x axis. Its position varies with time according to x = t + 4.0t³, where x is in meters and t is in seconds.

(a) Find the kinetic energy of the particle at any time t. (Use the following as necessary: t.)

(b) Find the magnitude of the acceleration of the particle and the force acting on it at time t. (Use the following as necessary: t.)

(c) Find the power being delivered to the particle at time t. (Use the following as necessary: t.)

(d) Find the work done on the particle in the interval t = 0 to t = 1.50 s.

Answer 1

To get started...

Kinetic energy is (1/2) * m * v**2 (v**2 means v squared)

So, you need the velocity---you are given the equation for distance as a function of time. take the differential of this to get velocity:

x = t + 4 * t**3

v = dx/dt = 12 * t**2

Looking ahead, you also will be needing acceleration:

a = dv/dt