How do I remember which formulas to use when studying 1-D Kinematics?

I know that I need x (position), v (velocity), and t (time), but I don't understand what x_o, V_x, V_xo, and A_x mean, or what formulas to use to find each one.

2 Answers
Oct 17, 2017

See below.

Explanation:

Generally used kinematic equations :

  • s_f=s_i+v_(is)Deltat+1/2a_s(Deltat)^2

  • v_(fs)=v_(is)+a_sDeltat

  • v_(fs)^2=v_(is)^2+2a_sDeltas

Where:

  • s_f is the final position
  • s_i is the initial position
  • Deltat is the time interval over which the motion occurred, where Deltat=t_f-t_i
  • Deltas is the change in position over the motion, where Deltas=s_f-s_i
  • v_i is the initial velocity
  • v_f is the final velocity
  • a_s is the acceleration of the object in the direction of the position you are measuring (i.e. a_y if you are looking at an object moving vertically or a_x if you are looking at an object moving horizontally)

Here it seems the preference of your teacher is to use v_0 for initial velocity and v for the "final" or current velocity. We would then have:

  • s=s_0+v_(0s)Deltat+1/2a_s(Deltat)^2

  • v_s=v_(0s)+a_sDeltat

  • v_s^2=v_(0s)^2+2a_sDeltas

So, for you:

  • x_0 is the initial x position
  • V_x is the final or current horizontal or x velocity
  • V_(x0) is the initial horizontal velocity
  • A_x is the horizontal acceleration

Which equation you use will depend on which variable you are trying to solve for.

For example:

  • If you're looking for the change in position but don't have time, you would use the third equation
  • If you're looking for change in position and you do have time, but you don't know anything about the final velocity, you would use the first equation

etc.

Oct 17, 2017

I think a good technique would be to list all the factors you have in a horizontal row.

Explanation:

You fill in for each factor/variable the value and the units. One variable will be missing and one not mentioned at all in the data. Put a question mark beneath the factor you are told to find and a horizontal dash under the irrelevant one.

Each of the kinematic equations is missing one of the variables, look through them carefully and you'll see what I mean. This is how to decide which equation to use when you are starting out, with enough practice it does become obvious (promise!)