Power, Work, Kinetic Energy Problem

[yb1013]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

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

 

[Queue]

Homework Statement

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.

Homework Equations

I'm pretty that equations aren't normal variable equations aren't used here because I'm asked for expressions, not just a numerical value.

The Attempt at a Solution

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

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).

 

[yb1013]

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

 

[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?

 

[yb1013]

ok i think i got it, thank you