1D Kinematics

  • Thread starter PFuser1232
  • Start date
  • #1
479
20

Main Question or Discussion Point

Usually, equations of motion (with constant acceleration) are written in terms of values of position/velocity at time ##t=0##.
Take for example:

$$x = x_0 + v_0t + \frac{1}{2} a t^2$$

Where ##x_0## and ##v_0## are the values (at ##t=0##) of position and velocity respectively.

What if we're given position at some other time ##t=t_0##, instead of ##t=0##, and we're asked to find ##x## as a function of time?

What I do is I find a more general form of the equation I wrote above as follows:

$$\int_{x_0}^x dx' = \int_{t_0}^t v(t') dt'$$

Where ##x_0## now represents position at time ##t=t_0##.

Another way would be to eliminate the variable ##x(0)##

Is there any alternative approach?
 
Last edited:

Answers and Replies

  • #2
19,805
4,050
This approach is great. Of course, what you would find is that you could also just substitute (t - t0) for t in the original equation (i.e., shift the time scale), assuming that v0 is the velocity at t = t0.

Chet
 

Related Threads for: 1D Kinematics

  • Last Post
Replies
2
Views
467
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
6K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
569
Replies
1
Views
596
Replies
2
Views
1K
Top