Acceleration: distance, s, in metres, m

The idea

Distance, s, is the length of the path travelled by an object, measured in metres (m). It is a scalar quantity, so it has magnitude only and no direction. In acceleration problems, s usually means the distance moved during the time interval over which the acceleration acts. For example, using v² − u² = 2 × a × s, if a car accelerates from 0 to 10 m/s at 2 m/s², s = 100 ÷ 4 = 25 m. Distance is not the same as displacement: displacement is the straight-line distance in a stated direction. Convert units before substituting: 250 cm = 2.5 m and 1.2 km = 1200 m. On a velocity–time graph, distance travelled equals the total area between the line and the time axis, treating all areas as positive.

What earns the marks

• State that s is the distance travelled along the path and is measured in metres, m.
• Recognise that distance is a scalar quantity, having magnitude but no direction.
• Convert distances given in cm, km or mm into metres before substitution.
• Calculate distance for uniform acceleration using v² − u² = 2 × a × s when u, v and a are known.
• Find distance from the area under a velocity–time graph, treating all areas (even those below the time axis) as positive path lengths.
• Distinguish distance s from displacement, which includes direction and treats areas below the time axis as negative.

Common mistakes and how to put them right

• Confusing distance with displacement.

  Put it right by noting that distance is scalar and displacement is a vector.

• Forgetting to convert cm or km to m.

  Put it right by dividing cm by 100 or multiplying km by 1000.

• Treating areas below the time axis as negative when calculating distance.

  Put it right by adding the absolute values of all areas to find total distance.

Exam tips

• Write the unit m with every distance value and check that all quantities are in SI units before calculating.
• For velocity–time graphs, split the area into rectangles and triangles, then add their absolute values to find total distance s.
• Remember that distance can never be negative; if a calculation yields a negative value for distance, check your signs for acceleration and displacement.