Classical Mechanics - finding displacement with given force

  • #1
3
0

Homework Statement


- The force acting on a particle m = 3kg is given by the following force equation: F = (v/9)(3 - x2),
the particle begins at a position of x = 1m with a speed of v = 0 m/s at time t = 0s. Find the displacement of the particle at time t = 5 s.

Homework Equations


F = m(dv/dt) or F= m(dv/dx)(v)

The Attempt at a Solution


Our professor set up the problem wrong, so he said all we have to do is get to the integral where we'd find x and stop.
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,874
1,655
Welcome to PF;
... so what did you do?
 
  • #3
3
0
Welcome to PF;
... so what did you do?
Well I tried it two ways, neither of which I thought was right...
n=7vks70HEUV82ikRKq9lDD9E1%2b0Mw0NDmL%2ftM1%2fH%2b4p0%3d&docid=016fc1db036ef4106b07348020be72487.jpg

token=YcoBfb2774deTF3wZ6MaQrYbVQ%2fvPYwJAM%2faX8w795U%3d&docid=0155b644af83a49af8eeec1a8acd84697.jpg
 
  • #4
Simon Bridge
Science Advisor
Homework Helper
17,874
1,655
In the first page, you cannot take the x's outside the integral over t because x is a function of time.
On the second page, you, instead, tried changing the variable ... that seems reasonable to me.
You'll end up with an implicit equation for x(t) but you only need x at a particular time.
 
  • #5
3
0
In the first page, you cannot take the x's outside the integral over t because x is a function of time.
On the second page, you, instead, tried changing the variable ... that seems reasonable to me.
You'll end up with an implicit equation for x(t) but you only need x at a particular time.
So on the 2nd page you would end up with -(1/3)x3t + 3xt - (8/3)t ?
 
  • #6
Simon Bridge
Science Advisor
Homework Helper
17,874
1,655
No - remember, the x terms are not constants in time.
You have to integrate the x terms wrt x.
 

Related Threads on Classical Mechanics - finding displacement with given force

  • Last Post
Replies
2
Views
756
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
4K
Replies
2
Views
3K
  • Last Post
2
Replies
37
Views
1K
Replies
14
Views
891
Replies
3
Views
6K
Replies
4
Views
304
Replies
7
Views
6K
Top