Motion Graphs
- Three types of graph that are used to represent motion are displacement-time graphs, velocity-time graphs and acceleration-time graphs
- Graphs are named 'y-axis - x-axis', so 'displacement-time' simply means 'displacement on the y-axis and time on the x-axis'
- Graphs of motion can be thought of as telling a story of something which has happened in the real world, such as
- the time, direction and average speed of a journey to school
- initial and final velocity and acceleration as a rocket takes off from the launchpad
- movement and speed in various directions as an athlete takes part in an event
- Interpreting graphs means using the slope of the line, or the area under the line to find information about that 'story'
- Drawing graphs is a skill where careful planning, plotting and line drawing from some data yields further information from an investigation
Displacement-Time
- On a displacement-time graph;
- Slope equals velocity
- A straight (diagonal) slope represents a constant velocity
- A curved slope represents an acceleration
- A positive slope represents motion in the positive direction
- A negative slope represents motion in the negative direction
- A zero slope (horizontal line) represents a state of rest
- The area under the curve is meaningless
- Slope equals velocity
Velocity-Time
- On a velocity-time graph…
- Slope equals acceleration
- A straight line represents uniform acceleration
- A curved line represents non-uniform acceleration
- A positive slope represents an increase in velocity in the positive direction
- A negative slope represents an increase in velocity in the negative direction
- a zero slope (horizontal line) represents motion with constant velocity
- The area under the curve equals the displacement or distance travelled
- Slope equals acceleration
Acceleration-Time
- On an acceleration-time graph…
- A zero slope (horizontal line) represents an object undergoing constant acceleration
- The area under the curve equals the change in velocity
- The steepness of the slope is meaningless
How displacement, velocity and acceleration graphs relate to each other
Drawing Graphs
- Drawing a good graph is an important skill
- Good graphs have the following:
- Each axis has two labels; the name of the variable and the unit (and may include a multiplier, for example, m × 10−9)
- Values on the axes are evenly spaced, with the same number of divisions for each amount
- The axes start at the origin only when this fits the data or the relationship being graphed is directly proportional or when specified in the question
- Increments on the scale are in multiples of 2, 5 and 10 but never multiples of 3.
- The range of values being plotted takes up the length of the axis, so that the plotted line takes up most of the space on the graph
- Plots are accurate to within half a small square
- Plots and curves are drawn with sharp pencil so that they are narrow (don't take up more than half a small square)
- Lines of best fit match the data, so that lines go through as many of the plots as possible (ignoring outliers) with the remainder evenly spaced above and below the line
Exam Tip
Interpreting Graphs
It's common for a question to ask you to solve something 'using a graphical method'. This just means 'by finding your answer on a graph'.
In AS Physics most (but not all) graphs will be a straight line, meaning they follow the equation y = mx + c
This means that the 'graphical method' question is asking you to look at the gradient, or the area under the line. Once you are secure in finding these then graph questions will become much easier!
Drawing Graphs
A well-drawn graph will net you four or five quick and easy marks IF you have practiced the skill.
Common mistakes are starting at the origin when there is no need (so the line takes up less than half of the page) and trying to work with a scale that goes in multiples of three (making it hard to get the plotting right).
