Formula Grids · Mechanics · M-01

v = s / t Speed

Calculation grid60 cellsTarget: 6 min

\(v = \dfrac{s}{t}\)

\(v\): (average) speed in m/s  ·  \(s\): distance in m  ·  \(t\): time in s

  • Average speed = total distance ÷ total time.
  • Units are in the column and row headings, so write numbers only in the cells.

A Find the speed \(v\) \(v = s \div t\)  (answers in m/s)

time ↓  distance → 10 m20 m50 m100 mthere and back:
30 m each way
1 s
2 s
5 s
10 s

Notice: Down a column, the time doubles, so the speed . In the last column, use the total distance.

B Find the distance \(s\) \(s = v \times t\)  (answers in m)

speed ↓  time → 0 s2 s4 s10 s2 min
1 m/s
2 m/s
3 m/s
5 m/s

Notice: Across a row, \(s\) grows in step with \(t\) (the speed is constant). In the last column, change minutes to seconds first.

C Find the time \(t\) \(t = s \div v\)  (answers in s)

speed ↓  distance → 10 m20 m40 m100 m1 km
1 m/s
2 m/s
5 m/s
10 m/s

Notice: Faster means less time. Compare the rows for 1 m/s and 10 m/s: the speed is ×10, the time is .

Think about it Concept check · circle one answer

Concept: average speed

1. A car travels 100 m in 10 s. Which must be true?

  1. always 10 m/s
  2. average 10 m/s
  3. it never stopped
  4. it sped up

\(s/t\) gives the average speed. The car may have sped up, slowed down or stopped on the way.

Concept: distance vs. displacement

2. A runner runs once round a 400 m track in 50 s. The average velocity is

  1. 8 m/s
  2. 0 m/s
  3. 4 m/s
  4. 400 m/s

The runner ends where they started, so the displacement is 0 and the average velocity is 0. The average speed is 8 m/s.

Concept: how \(t\) depends on \(v\)

3. The distance stays the same and the speed doubles. The time taken

  1. doubles
  2. stays the same
  3. halves
  4. becomes ¼

\(t = s/v\): with \(s\) fixed, \(t \propto 1/v\). Double the speed → half the time (grid C).

Formula Grids · M-01 v = s / t · Set 1Calculator: not needed