The Kinematics Formula
Whether you are calculating the trajectory of a train, the pace of a marathon runner, or the speed of sound, the relationship between distance, speed, and time is one of the most fundamental principles in physics and basic algebra. The foundational formula connecting these three distinct physical properties is Distance = Speed × Time (\( d = s \times t \)).
The Magic Triangle
To easily remember how to rearrange the formula depending on which variable is missing, mathematicians and science teachers frequently use the "Magic Triangle." In this visual aid, Distance (\( d \)) sits at the top peak, while Speed (\( s \)) and Time (\( t \)) sit side-by-side at the bottom base.
- To find Distance: Cover the 'd'. The remaining variables are 's' and 't' side-by-side, indicating multiplication: \( d = s \times t \).
- To find Speed: Cover the 's'. You are left with 'd' directly over 't', indicating division: \( s = \frac{d}{t} \).
- To find Time: Cover the 't'. You are left with 'd' directly over 's', indicating division: \( t = \frac{d}{s} \).
Unit Conversions
The most common error students make in kinematics word problems is failing to synchronize their units of measurement. If your speed is given in miles per hour (mph), your time variable must strictly be calculated in hours, and your resulting distance will inherently be in miles. If a word problem gives you a speed in mph but a time in minutes, you must mathematically convert the minutes into hours (by dividing by 60) before plugging the values into our calculator.