Speed: s = v t

The idea

This is the symbolic form of distance travelled = speed × time, where s is distance, v is speed and t is time. The symbols allow quick rearrangement: v = s ÷ t and t = s ÷ v. For example, a cyclist at 6 m/s for 25 s travels s = 6 × 25 = 150 m. The equation applies to steady motion in a straight line; for changing speed it gives average speed. Keep units consistent: s in metres, v in metres per second, t in seconds. When using the symbols, write the rearranged equation before substituting values, and give the final answer with its unit.

What earns the marks

• Identify each symbol correctly: s = distance, v = speed, t = time.
• Substitute numerical values into s = v t and evaluate accurately.
• Rearrange to v = s ÷ t or t = s ÷ v when the unknown is speed or time.
• Use consistent SI units (m, m/s, s) and convert where necessary.
• Present the final answer with the correct unit and appropriate precision.
• Apply the equation to real contexts such as vehicles, runners or sound travelling through air.

Common mistakes and how to put them right

• Confusing s (distance) with speed.

  Put it right by remembering s stands for distance and v for speed.

• Substituting time in minutes directly into s = v t.

  Put it right by converting time to seconds first.

• Rearranging incorrectly, for example writing t = s v instead of t = s ÷ v.

  Put it right by dividing both sides by v.

Exam tips

• Write the symbol equation and the rearranged form before putting numbers in.
• Keep units with the numbers throughout the calculation to help spot errors.
• Round only at the end and give the unit, for example 150 m, not just 150.