Distance, Speed and Time Calculations

The fundamental equation for constant speed is:

$v = \frac{d}{t}$

This rearranges to:

$d = vt \qquad t = \frac{d}{v}$

Single-stage problems

If a car travels 150 km in 2.5 hours:

$v = \frac{150}{2.5} = 60 \text{ km/h}$

Multi-stage problems

For journeys with different stages, calculate each stage separately.

Example: A cyclist rides 12 km at 16 km/h, then 8 km at 12 km/h.

Stage 1: $t_1 = 12/16 = 0.75$ h

Stage 2: $t_2 = 8/12 = 0.667$ h

Average speed $= \frac{\text{total distance}}{\text{total time}} = \frac{20}{1.417} = 14.1$ km/h

The average speed is NOT the mean of the two speeds. It uses total distance divided by total time.

Unit conversions

To convert km/h to m/s, divide by 3.6: $72$ km/h $= 72/3.6 = 20$ m/s.

To convert m/s to km/h, multiply by 3.6.

Common errors and how to correct them

• Averaging speeds instead of using total distance over total time.
• Forgetting to include rest periods in the total time for average speed.
• Using inconsistent units (mixing km and m, or hours and seconds).

How to apply this in an exam

Always state the equation first, substitute values with units, then give the answer with the correct unit. Convert units before substituting.