Describing Motion Around Us
Position-time graphs
Draw and read position-time graphs.
Why a graph? A table of numbers is hard to read at a glance. A graph turns the same numbers into a picture of the motion.
What a position-time graph shows. Time goes along the bottom (the x-axis). Position (how far from O) goes up the side (the y-axis). Each point says: 'at this time, it was here'.
How to draw one.
- Draw the two axes, meeting at the origin.
- Choose scales that use the paper well. For Table 4.3: 5 small divisions = 1 s across, and 5 small divisions = 20 m up.
- Mark each (time, position) point.
- Join the points.
A straight line = steady speed. Table 4.3 (0, 20, 40 … 120 m at 0, 1, 2 … 6 s) gives a straight line. The object moves 20 m every second: equal steps in equal times. That is constant velocity.
A curve getting steeper = speeding up. Table 4.4 (0, 1, 4, 9, 16, 25, 36 m at 0, 2, 4 … 12 s) gives a curve that gets steeper. The object covers more ground in each interval, so its velocity is increasing.
Steepness tells the speed. Think of the line as a hill you roll down: on a steeper hill you go faster. In the same way:
- a steeper line = faster;
- a flat line (parallel to the time axis) = the position is not changing, so the object is at rest. A flat line at 40 m means it is standing still, 40 m from O.
Reading velocity from the graph. Take two points, A and B. Draw a right-angled triangle under them:
- the upright side (BC) = how much the position changed;
- the flat side (CA) = how much time passed.
Velocity = BC ÷ CA. This is called the slope of the line. From (2 s, 40 m) to (4 s, 80 m): 40 m ÷ 2 s = 20 m s⁻¹.
Careful. A position-time graph is not a map of the road. It shows how the position changes with time, not the route the object took.
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