The Basics - Simple Principles Of Motion

Distance is usually measured in metres ( SI units ) and is frequently represented by the variable d.
Time is usually measured in seconds and is represented by the variable t.
Speed is usually measured in metres per second ( m/s ) and is represented by v.
I use Vi and Vf to denote initial speed and final speed, respectively.
Remember that variables can be represented by any combination of letters, they are just names for quantities e.g. d = 55m, d = 0.3cm, potato = 43m, time-initial = 4s.

In all cases a movement is measured from a "reference point", if you measure the distance you walk to school from home you will measure from your house - which is the reference point in this case, it is the point from which you start measuring.

Standard International Units
When you are performing physics calculations you should always keep similar types of measurements in the same units. If you are performing a calculation with two masses which weigh 2kg and 2000g you should convert both of them into one unit type, either convert them into kilograms or convert them into grams. Do not mix units of measurement.

SI ( Standard International ) units are special conventions for measuring which simplify physics calculations considerably. The metre, second and kilogram are SI units. If you perform your calculation using the above standard units you will be able to refer to your answer's units by an alias, e.g. 88 kg/m/s² turns into 88 "Newtons".

Kinematics and motion lack space-saving shorthands for units you should nevertheless use SI units ( m, kg, s ) when practical. Whenever you do not use SI units make sure that your measurements are all in the units which you are using.

Basic Equations
Physics relies heavily on mathematics. When solving a problem involving physics you will need to convert words and events into mathematical concepts, this conversion results in an equation.

Speed Speed is the rate at which distance changes. How many distance units are passed during each unit of time?
speed = distance / time
v = d / t

Lets do an example:
A car travelled 50km in 120minutes while keeping a constant speed. What was its speed?

Before we start solving for the speed we need to convert our units into useable form. A car's speed will usually be represented in km/h, we need to convert the time of the trip into hours. We do this by dividing by 60, 120/60 = 2 hours.

Lets declare our variables
d = 50km
t = 2h
v = ? km/h

The speed is "how many kilometres are passed in one hour" and we come up with an equation to model that: v = d / t
We input our values into the equation:
v = 50 / 2
v = 25km/h

We always state the answer to the question in a sentence.
"The speed of the car during the trip was 25km/h".
Acceleration Acceleration is the rate of change in speed, how the speed differs from one moment to the next.
acceleration = speed / time
a = v / t

Also, the total acceleration undergone is widely thought of as the final speed - the initial speed, all divided by the time. This is a useful way to model acceleration because an object might have been already moving before it began accelerating.
a = (Vfinal - Vinitial) / t

Example
A car speeds up from rest up to 60km/h in 6.2 seconds, what is its average acceleration?

Convert all measurements into metres and seconds to prevent confusion and/or awkward result units.

t = 6.2s
Vinitial = 0m/s
Vfinal = 16.6m/s
a = ? m/s²

a = 16.6 / 6.2
= 2.677 m/s²

We need to round the answer to two Significant Digits ( what are significant digits? ) therefore our word answer will be "The car accelerates at the rate of 2.7 m/s²"