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An explanation of the kinematic formulas, when to use each one, and the connections between acceleration, final and initial velocity, displacement, and time.

This is a draft cheat sheet. It is a work in progress and is not finished yet.


Kine­mat­ics is the collective name for the unit that covers accele­ration, velocity, displa­cement, and time and how they relate to each other. It's important to understand the formulas in this unit because they will come back in later units, such as force and work.

Measur­ement Review

VF or VI

Speed, Velocity and Accele­ration

Speed, measured in meters­/se­cond, can be found with the formula:
distance / time
Velo­city, also measured in meters­/se­cond, can be found with the formula:
displ­acement / time, or Δx / Δt.
Acce­ler­ati­on, measured in meters­/se­con­d2, can be found with the formula:
(final velocity - initial velocity) / (final time - initial time), or (VF - VI) / (TF - TI)
Time, measured in seconds, is generally given to you.
TI is usually, but not always, zero.

The Four Formulas

Δx = VIt + ½ at2
VF = VI + at
Δx = (VF + VI / 2) × t
Δx = (VF2 - VI2) / 2a)
Every kinematics problem will give you 3 of the 5 variables and ask you to solve for 1 variable. The fifth variable doesn't matter - use the formula with­out that variable (if the problem doesn't mention a, use the formula without a in it.)

Example Problem

A worker drops a wrench from the top of a tower 80 m tall. What is the velocity when the wrench hits the ground?

In the context of this problem, we are told that Δx = 80 m. We know that VI = 0 m/s because at the beginning of the problem, the wrench wasn't moving (the worker was holding it. And we can assume that accel­eration is 9.8 m/s2 because grav­ity is taking effect.

This leaves us with VF and t. Since the question is asking us for final velocity, we know that t isn't important to this problem - therefore, choose the kinematic equation without the t in it to solve the problem.
The equation without t in it is Δx = (VF2 + VI2) / 2a. Then, all that's left to do is to plug in all the variables and solve for VF!

The answer to this problem should be 39.60 m/s.