lesson
Updated 6 days ago · 3 views
When a ruler slips between your fingers and you snap them shut, you can't measure your reaction time directly with a standard stopwatch. Instead, you measure a distance in centimeters—so how do exam questions expect you to turn that distance into seconds?
From Drop Distance to Reaction Time
In the early 1600s, Galileo Galilei demonstrated that all falling objects accelerate at the exact same rate under gravity near Earth's surface, roughly g=9.8 m/s2.
Because the ruler starts from rest (initial speed u=0), the distance fallen d is given by d=21gt2. Rearranging to solve for reaction time t gives:
t=g2d
📊A clean visual breakdown card showing the ruler drop equation. On the left, an illustration of a hand catching a ruler marked in centimeters, with an arrow showing drop distance 'd'. On the right, a formula card highlighting two steps: Step 1: Convert distance from cm to meters (d in m = d in cm ÷ 100). Step 2: Plug into t = √(2d / 9.8). Color palette: dark blue text (#1e2945), white card backgrounds (#ffffff) on light gray (#f8f9fa), bright blue accents (#22b7ff). Responsive layout fitting within 350px width.
Let's work through an example: a student catches the ruler at the 19.6 cm mark.
First, convert centimeters to meters by dividing by 100: 19.6 cm=0.196 m. Then substitute d=0.196 m and g=9.8 m/s2 into the formula:
t=9.82×0.196=9.80.392=0.04=0.20 s
A common mistake here is plugging centimeters directly into the formula without converting to meters first. If you use 19.6 instead of 0.196, your calculated time will be ten times too large.
What happens when you repeat this test multiple times and one of the measurements looks completely out of place?
Spotting Anomalies and Calculating the Mean
An anomaly (or outlier) is an experimental result that does not fit the pattern of the other repeat readings, often caused by a loss of focus or slipping.