# Power, Work, Kinetic Energy Problem

1. Mar 16, 2009

### yb1013

1. The problem statement, all variables and given/known data

A 4.60 kg particle moves along the x axis. Its position varies with time according to x = t + 1.8t3, where x is in meters and t is in seconds.

(a) Find the kinetic energy at any time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.)

(b) Find the acceleration of the particle and the force acting on it at time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.)

(c) Find the power being delivered to the particle at time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.)

(d) Find the work done on the particle in the interval t = 0 to t = 2.00 s.

2. Relevant equations

Im pretty that equations arent normal variable equations arent used here because im asked for expressions, not just a numerical value.

3. The attempt at a solution

I've tried to fiddle around a little bit, but ive basically just made a mess of wrong answers... can someone please help me out here. Im very confused even on where to start on this question.

2. Mar 16, 2009

### Queue

I'm going to guess that's x(t) = t + 1.8t3... Well it's velocity as a function of time is v(t) = 1 + 5.4t2 and acceleration is a(t) = 10.8t both by differentiation.

Thus kinetic energy is given by KE = .5mv2.

Acceleration is given by what is above (the double derivative of x(t). F = ma.

What does power mean? Work from that definition.

Try the work/kinetic energy theorem for the the last part but you need initial conditions (namely initial velocity).

3. Mar 16, 2009

### yb1013

hmmm, I understood your first two explanations, but still kinda puzzled about the last 2... can you use Power = W/t

4. Mar 16, 2009

### Queue

The last two are tied together.

If you do P = W/t then you need to calculate work.

W = $$\Delta KE = KE_{final} - KE_{initial}$$. But to find KE you need a velocity which for some reason I thought needed a given value for t=0 but it's just v(0) = 1+5.4t2 = 1 m/s.

Good?

5. Mar 16, 2009

### yb1013

ok i think i got it, thank you