Calculating Work Done on a Particle Using Basic Formulas

[Jrlinton]

Homework Statement

A single force acts on a 3.3 kg particle-like object in such a way that the position of the object as a function of time is given by x = 2.1t - 1.4t2 + 1.7t3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 4.8 s.

Homework Equations

Basic work formulas

The Attempt at a Solution

So i found the distance of the movement by plugging 4.8 for t and got 165.83 m, found the second derivative of the position formula to get the acceleration function, got 46.16m/s/s at 4.8s. I multiplied these quantities as well as the mass to get 25260.6 J. This was obviously wrong

 

[berkeman]

Homework Statement

A single force acts on a 3.3 kg particle-like object in such a way that the position of the object as a function of time is given by x = 2.1t - 1.4t2 + 1.7t3, with x in meters and t in seconds. Find the work done on the object by the force from t = 0 to t = 4.8 s.

Homework Equations

Basic work formulas

The Attempt at a Solution

So i found the distance of the movement by plugging 4.8 for t and got 165.83 m, found the second derivative of the position formula to get the acceleration function, got 46.16m/s/s at 4.8s. I multiplied these quantities as well as the mass to get 25260.6 J. This was obviously wrong

Are you familiar with the integral formula for calculating the work?

 

[Jrlinton]

Yes but I am ignorant as to how that would work with the givens being position and mass

 

[ramzerimar]

You have a variable force. How do you find work done if you have a variable force acting on a particle?

EDIT: First, what's the expression for the force acting on the particle?

 

[berkeman]

Yes but I am ignorant as to how that would work with the givens being position and mass

Well then please show them to us and start working with the equations. That will help us a lot in helping you. If you can use LaTeX in your posts of the equations, that would be best. I'll find the link to the PF tutorial on LaTeX equations in a sec...

 

[berkeman]

I'll find the link to the PF tutorial on LaTeX equations in a sec...

From INFO, Help/How To: https://www.physicsforums.com/help/latexhelp/