Biomechanical principles: Speed, distance.

The idea

Speed and distance are scalar quantities used to describe linear motion in sport. Distance is the total length of the path a performer travels, measured in metres (m), and it has magnitude only. Speed is the rate of change of distance with respect to time, calculated as speed = distance ÷ time, so its unit is metres per second (m s⁻¹). For example, a 400 m runner who completes one lap in 50 s has covered a distance of 400 m and has an average speed of 400 ÷ 50 = 8 m s⁻¹. Distance is not the same as displacement, which is a vector measured in a straight line from start to finish. Speed is not the same as velocity, which is a vector. In biomechanics, average speed over a whole movement is found by dividing total distance by total time, while instantaneous speed is the speed at a particular moment.

What earns the marks

• Distance is a scalar quantity: it is the total length of the path travelled and has magnitude only.
• Distance is measured in metres (m).
• Speed is a scalar quantity: it is the rate of change of distance with respect to time.
• Speed is calculated using speed = distance ÷ time.
• The unit of speed is metres per second (m s⁻¹).
• Average speed uses total distance divided by total time; instantaneous speed is the speed at a given moment.
• Distance differs from displacement, which is a vector measured in a straight line from start to finish.
• Speed differs from velocity, which is a vector quantity.

Common mistakes and how to put them right

• Treating distance and displacement as the same quantity.

  Put it right: Distance is the total path length (scalar), whereas displacement is the straight-line distance from start to finish with direction (vector).

• Confusing speed with velocity.

  Put it right: Speed is scalar and has magnitude only, whereas velocity is a vector and includes direction.

• Using the wrong unit for speed, such as m or m s.

  Put it right: Speed is measured in metres per second (m s⁻¹).

• Dividing time by distance instead of distance by time.

  Put it right: Speed = distance ÷ time, so a 100 m swim in 80 s gives 100 ÷ 80 = 1.25 m s⁻¹.

Exam tips

• Check whether the question asks for distance, displacement, speed or velocity before selecting an answer, because scalar and vector quantities are often offered as distractors.
• For calculation items, write the equation speed = distance ÷ time, substitute the values with units, then state the answer in m s⁻¹.
• If a graph or split times are given, remember that average speed uses total distance ÷ total time, not the speed of the fastest section.