SCool Revision Summary
SCool Revision Summary
Vectors Versus Scalars
Vectors and scalars are two types of measurements you can make.
 A scalar measurement only records the magnitude (or amount) of whatever you are measuring.
 A vector measurement records the magnitude of the thing you are measuring and the direction.
Vector Addition
Adding scalars is easy because you can just add the numbers.
For Example: 3kg + 4 kg = 7 kg
Adding vectors needs much more care. You have to take into account their magnitude and direction.
For Example: What's 3N + 4N? Well, it depends on the directions! Look at the possibilities...
or
Note: 1N is not balanced
or
So in other words, you add vectors geometrically (using geometry). You should be able to do this using accurate diagrams (don't forget your protractor) or by using Pythagoras.
Resultant Vectors
The resultant vector is the one that you get when you add two or more vectors together. It is a single vector that has the same effect as all the others put together. Finding the resultant vector when the forces are in different directions can be tricky if you don't like Pythagoras, so here's a couple to get you going!
Worked Example:
Using Pythagoras: R^{2} = 8^{2} + 7^{2}
So, R = √113 = 10.6 N
Resolving Vectors into Components
We have just shown that any two vectors can be represented by a single resultant vector that has the same effect. Guess what?! You can do the same thing in reverse! Any single vector can be represented by two other vectors (components), which would have the same effect as the original one:
You need to use trigonometry to find the two components of a vector. Remember the two components will always be at right angles.
Check that you understand how to calculate the values of the components.
Speed and Velocity
Both speed and velocity tell us how far something is travelling in unit time. As velocity is a vector it must also tell us what direction the object is travelling in.
Speed (m/s) = 
distance moved (m)
time taken (s)

Velocity (m/s) = 
displacement change (m)
time taken (s)

Acceleration
Acceleration tells us how rapidly something is changing speed  for instance, the change in speed in unit time. Deceleration is the same thing, but we give it a negative sign as the speed will be decreasing.
Acceleration (m/s^{2}) = 
Change in velocity (m/s)
time taken (s)

Displacementtime graphs
These show the motion of an object very clearly and allow you to find position and velocity at any time. Any graph that you see will be a combination of these sections.
Notice that the gradient =

Change in D
Change in t

= the velocity at any time. 
When the velocity is changing, as on the lower two graphs, you can find the velocity at any point by drawing a tangent touching the graph at that point by drawing a tangent touching the graph at that point and working out its gradient using the same equation.
Velocitytime graphs
These fare similar to displacementtime graphs, but this time velocity is on the yaxis. Here are the only possibilities that you'll come across at Alevel.
Notice that the gradient =

Change in velocity
Change in time

= acceleration or deceleration. 
You also need to know that the area under the line gives you the displacement of the object up to that point.
Accelerationtime graphs
Note: All three of the movement graphs are related to each other as the:
 Gradient of D/t graph gives you the points on the v/t graph.
 Gradient of v/t graph gives you the points on the a/t graph.