The Reaction Ruler

Lesson 8 of 10 · 7 min · Free, no account needed

What you will learn

From rest, the distance fallen is d = ½ g t²: the area of the triangle under the speed graph.
In equal time steps the gaps grow 1, 3, 5, 7, so the total grows 1, 4, 9, 16: like the square of the time.
Read it backwards and a caught ruler tells your reaction time: about 20 cm means about 0.2 s.

Catch the falling ruler. The centimetre where you grab it is your reaction time. How?
Three tries. Your best one counts.
Slow motion: a flash every 0.05 s while the ruler falls.
Press Step four times. Watch the gaps column.
Why squares? Drag the time line on the ruler's speed graph.
The green triangle is the area under the speed line. Watch the ruler next to it.
The rule for a fall from rest.
Speed after t seconds: v = g t. The graph is a straight line through zero.
Distance is the triangle's area: ½ × t × g t, so d = ½ g t².
Twice the time, four times the distance. Simplified model: no air, which is fine for a ruler.
Now find your reaction time: set the time so the ruler falls to your catch mark.
The green mark is your best catch from the start of the lesson.
A stone falls from a 15 m roof. How long until it lands?
Set the stopwatch to your estimate.
From math: draw distance fallen against time through the dots.
The dots come from the falling tower. What shape is it?
A friend catches the ruler at 45 cm. What is their reaction time, in seconds?
d = ½ g t², so t = √(2d ÷ g). Use d = 0.45 m.
Your reaction time, behind the wheel at 50 km/h.
Play both cars.

Lessons are interactive and need JavaScript. Turn it on to play them.