Question

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.

Answer 1

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.

Answer 2

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!)