PHYSICS WORTH SHARING
Most of the US set the clocks back on Sunday. Sunset now comes an hour earlier by the clock, so a lot of drives home from practice, games and work now end in the dark.
Here is a question for your students. Something steps into the road. How far does the car travel before the driver even touches the brake?
At 20 m/s (about 45 mph), the answer is about 30 meters. That is six or seven car lengths, and the car has not slowed down at all yet.
FREE THIS WEEK
Reaction Distance practice sheet (Unit 1: Motion). One printable page, six problems with whole-number answers, built on v = d / t and a = (vf − vi) / t with our GUESS steps. Page 2 is the answer key, with a teacher note and the ruler-drop conversion chart for the demo below. Get the free Reaction Distance practice sheet
Big idea
Reaction time is everything that happens between seeing a problem and pressing the brake: noticing it, deciding what to do and moving your foot. Until the brakes engage, nothing new is acting to slow the car down. So for that whole stretch the car keeps moving at the same velocity, and the distance it covers is simply d = v × t.
Run the numbers. A 1.5 s reaction at 20 m/s covers 30 m. At 30 m/s (about 67 mph), the same 1.5 s covers 45 m. Same reaction time, 1.5 times the speed, 1.5 times the distance. Reaction distance is proportional to speed.
What sets the reaction time? Mostly expectation. A widely cited review of driver studies by human factors researcher Marc Green estimates about 0.7 s when a driver expects to brake, about 1.25 s for a common signal like brake lights ahead, and about 1.5 s for a surprise, like something entering the road. In the dark, the noticing step can take longer, because a pedestrian or cyclist is harder to see.
Braking distance then gets added on top of the reaction distance. That part grows even faster with speed, which is a story for another issue.
The ruler-drop reaction test (run it Monday)
For: Unit 1 Motion, v = d / t and free fall. Time: 5 to 10 minutes. Materials: one 30 cm ruler per pair.
Partner A holds the ruler at the top so it hangs straight down. Partner B holds a thumb and finger open at the 0 cm mark, not touching it.
Sometime in the next 5 seconds, without warning, A lets go. B catches it. Record the centimeter mark at B's fingers. Do three trials.
Convert with the chart: 5 cm is about 0.10 s, 10 cm about 0.14 s, 15 cm about 0.17 s, 20 cm about 0.20 s, 25 cm about 0.23 s and 30 cm about 0.25 s. The ruler falls freely from rest, so the chart is just d = ½gt² solved for t, with g = 9.8 m/s².
Make it a car. Multiply your reaction time by 20 m/s. A 0.2 s catch means 4 m of travel before braking.
Round 2: the catcher counts backward by threes from 100, out loud, while waiting to catch. Compare the results.
Land it: ask why a surprised driver needs about 1.5 s when the ruler catch takes about 0.2 s. In the ruler test you know exactly what is coming and exactly what to do. On the road you first have to notice, understand and decide.
One quick question
One tap. It helps us decide what to make next.
What are you teaching in the next two weeks?
For your classroom
The practice sheet uses the same equations and GUESS steps as our Motion Unit Bundle: four editable slide decks (Motion Introduction, Graphing Motion, Acceleration and Gravitational Acceleration), four practice assignments, 10 warm-ups, a position vs time scavenger hunt, a crossword review, a unit test and answer keys. See the Motion Unit Bundle
In case you scrolled past it: get the free Reaction Distance practice sheet.
Sources: Eric Chudler, Neuroscience for Kids, Reflexes (ruler reaction test and chart) and Marc Green, What Is Driver Reaction Time?, which summarizes his 2000 review of driver perception-brake times.
Forward this to a colleague who is teaching Motion this fall.
Stay Wildly Curious — Lauren & Shawn
