Describing Motion

Position

In order to describe how objects move, we need to know and understand their positions.
The easiest way to determine this is by drawing the objects on a coordinate grid.
Their position can be described according to a certain reference point.

For example an objects position could be (-3, 4) from a zero point. By plotting those coordinates down in a grid with the axes along the cardinal directions (x-axis is east and west and the y-axis is north and south) it becomes easy to tell that the object is three units to the west and four units to the north.

For example if you drive a car to the grocery store which is 4 kilometers away, your distance might be around 5 kilometers due to all the twists and turns you will have made along the way.

Displacement describes the change in position from one point to another in a straight line.
Distance is a vector quantity.
Displacement does not account for changing of paths.

For example if you took the same trip in your car to the grocery store, while your distance might be 5 kilometers or more, your displacement would only be 4 kilometers.
Likewise, if you go on a bike trip and travel 5 kilometers away from your home and make the same trip back, your distance traveled would be 10 kilometers. However, your displacement would be 0 kilometers as you'll have ended up in the same position as you started!

Similarly, velocity and speed are two vector and scalar quantities that describe similar phenomena.

Acceleration is the increase or decrease in an object's velocity.
It is a vector quantity that measures the change in velocity over change in time.
This means that acceleration measures the change in displacement over change change in time over change in time.
Thus it can be written as meters divided by seconds squared, or ms⁻².
Acceleration can be positive or negative, depending on the change in velocity.
For example if you slow down by 5 m/s then the change in velocity is -5 ms⁻¹

An object with increasing velocity in the positive direction has positive acceleration.
An object with decreasing velocity in the positive direction has a negative acceleration.

An object with decreasing velocity in the negative direction has positive acceleration.
An object with increasing velocity in the negative direction has a negative acceleration.

Graphs can describe the motion of an object.
A time-displacement graph shows how the displacement of an object changes over time.

The gradient of a line gives you the rate of change.
For example a gradient of 3 for a time (seconds) displacement (meters) chart would mean that the rate of change is 3 meters of displacement every second.

Creating shaded areas can help us find certain components of the graph by calculating the area.

The green area shows displacement as velocity (m/s) multiplied by time (s) gives meters.

Throughout a time frame, velocity can vary, thus the average can be found by dividing the total displacement by the total time spent.

Instantaneous values can be found from graphs.
In a graph with a constant gradient (straight line), instantaneous values can be found by locating any point on the line. Thus the gradient is the value.
However graphs aren't always constant (curved line).
In this scenario a tangent line should be drawn based on a point in the graph.
Calculating the gradient of this tangent line gives us the instantaneous value for that point.

Motion can either have no acceleration, meaning that the velocity is constant, uniform accelerating, meaning that velocity constantly increases, or non-uniform acceleration, meaning that the velocity increases or decreases varyingly.

In the picture above, A represents an object with no acceleration, B represents an object with uniform acceleration and C represents an object with non-uniform acceleration.