Calculating Speed

The relationship between speed, distance, and time is expressed by the primary formula: $v = \frac{d}{t}$ where $v$ represents speed, $d$ represents distance, and $t$ represents time.

This formula can be algebraically rearranged to solve for any of the three variables depending on the known information: $d = v \times t$ and $t = \frac{d}{v}$.

A Formula Triangle is a common visual mnemonic used to remember these relationships: placing Distance at the top and Speed and Time at the bottom helps visualize that distance is the product of the others, while speed and time are quotients.

Step 1: Identify Knowns: Extract the numerical values for distance and time from the scenario, ensuring you distinguish between the total journey and specific segments.

Step 2: Unit Verification: Check if the units for distance (e.g., km) and time (e.g., hours) are compatible with the required output unit (e.g., km/h). Perform conversions before calculating if necessary.

Step 3: Apply Formula: Substitute the values into $v = d/t$. If calculating average speed for a multi-part journey, sum all distances and all times first: $v_{avg} = \frac{\sum d}{\sum t}$

Step 4: Sanity Check: Evaluate the result to ensure it is physically plausible (e.g., a person walking at 50 m/s is likely a calculation error).

Watch the Units: Examiners frequently provide distance in kilometers and time in minutes but ask for the answer in km/h. Always convert minutes to hours by dividing by 60 before using the formula.

The 'Total' Rule: For complex problems involving multiple stages, never average the speeds of each stage. Always find the Total Distance and Total Time for the entire journey to find the correct average speed.

Rearranging Errors: If you struggle with algebra, use the formula triangle. Cover the variable you want to find, and the remaining variables show you the operation (top/bottom = divide, side-by-side = multiply).

Rounding Precision: Keep intermediate values in your calculator to avoid rounding errors, and only round the final answer to the requested number of decimal places or significant figures.

Mixing Units: A common mistake is calculating speed using mixed units, such as meters and minutes, resulting in 'meters per minute,' which may not be the standard unit required.

Zero Displacement vs. Distance: In speed calculations, only the total path length (distance) matters. Even if an object returns to its starting point (zero displacement), its speed is calculated based on the full distance traveled.

Time Representation: Decimal time is often confused with clock time. For example, 1.5 hours is 1 hour and 30 minutes, not 1 hour and 50 minutes. Always convert minutes to a decimal fraction of an hour ($min/60$) before calculating.