Define speed as distance travelled per unit time; recall and use the equation v = s/t

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – Motion: Speed

Cambridge IGCSE Physics 0625 – Topic 1.2: Motion

Objective

Define speed as distance travelled per unit time and recall and use the equation \$v = \frac{s}{t}\$.

Definition of Speed

Speed is a scalar quantity that describes how fast an object moves. It is the total distance travelled divided by the time taken.

Mathematically,

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

where

  • \$v\$ = speed (metres per second, m s⁻¹)

  • \$s\$ = distance travelled (metres, m)

  • \$t\$ = time taken (seconds, s)

Units and Conversions

The SI unit for speed is metres per second (m s⁻¹). In everyday contexts, kilometres per hour (km h⁻¹) is also used.

Conversion:

\$1\;\text{m s}^{-1}=3.6\;\text{km h}^{-1}\$

Rearranging the Formula

Depending on which quantity is unknown, the equation can be rearranged:

  • To find distance: \$s = v \times t\$

  • To find time: \$t = \frac{s}{v}\$

Worked Example

Problem: A cyclist travels 1500 m in 75 s. Calculate the cyclist’s speed.

  1. Identify the known values: \$s = 1500\;\text{m}\$, \$t = 75\;\text{s}\$.

  2. Use the definition \$v = \dfrac{s}{t}\$.

  3. Substitute the numbers:

    \$v = \frac{1500\;\text{m}}{75\;\text{s}} = 20\;\text{m s}^{-1}\$

  4. Result: The cyclist’s speed is \$20\;\text{m s}^{-1}\$ (or \$20 \times 3.6 = 72\;\text{km h}^{-1}\$).

Suggested diagram: A straight‑line track showing a start point, end point, distance \$s\$, and a stopwatch indicating time \$t\$.

Common Mistakes

  • Confusing speed (scalar) with velocity (vector).

  • Using the wrong units (e.g., mixing metres with kilometres without conversion).

  • Forgetting to convert time to seconds when the distance is in metres.

Quick Check Questions

  1. A car travels 120 km in 2 h. What is its speed in km h⁻¹ and m s⁻¹?

  2. If a runner’s speed is \$5\;\text{m s}^{-1}\$, how far will they run in 8 s?

  3. A train covers 300 m in 15 s. Calculate its speed and state whether it is faster or slower than \$10\;\text{m s}^{-1}\$.

Summary Table

QuantitySymbolFormulaSI UnitTypical Everyday Unit
Speed\$v\$\$v = \dfrac{s}{t}\$m s⁻¹km h⁻¹
Distance\$s\$\$s = v \times t\$mkm
Time\$t\$\$t = \dfrac{s}{v}\$sh

Key Points to Remember

  • Speed = distance ÷ time.

  • Always keep units consistent when using the formula.

  • Speed is a scalar; it has magnitude only, no direction.

  • Convert between m s⁻¹ and km h⁻¹ using the factor 3.6.