Describing Motion
Motion graphs and the kinematic equations
Read velocity off the slope of a position-time graph and displacement off the area under a velocity-time graph, and use v = u + at, s = ut + ½at² and v² = u² + 2as.
A table of positions and times tells you where something was. A graph of the same numbers tells you that at a glance, and then tells you two things the table did not: how fast the object was going, and how far it went. The trick is that both are hidden in the shape of the line rather than in any single point on it.
Slope and area
On a position-time graph the slope of the line is the average velocity. On a velocity-time graph the slope is the acceleration, and the area between the line and the time axis is the displacement. A line running flat along the time axis means no change in whatever is up the side: a stationary object on a position-time graph, zero acceleration on a velocity-time one.
Have a play
The parts of a position-time graph, each one named.
Tap any part of the picture.
Worked example
On a position-time graph, an object is at 40 m when the clock reads 2 s, and at 80 m when it reads 4 s. What is the magnitude of its average velocity?
Take the change up the side: the position went from 40 m to 80 m, a change of 40 m.
That is the top of the slope fraction — how much the quantity on the Y-axis changed.
Try it together
Now use the kinematic equations on a bus pulling away from a stop.
The bus starts from rest and holds a constant acceleration of 2.5 m/s² for 8 s. Answer with a bare number each time.
1.Use v = u + at. What is the bus's velocity after those 8 s, in m/s?
Have a go
Have a go on your own. A cyclist at 6 m/s brakes at a steady −1 m/s² until she stops. Use v² = u² + 2as. How far does she travel while braking, in metres?
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.