Average speed and distance

Calculating average speed

The speed of the trolley as it passes through the light gates only shows its speed at that particular moment. As it moves further down the ramp, its speed changes due to acceleration. Sometimes, it is necessary to calculate the average speed for the whole journey.

average~speed = \frac{total~distance~travelled}{total~time~taken}

This is when:

  • distance travelled is measured in metres (m)
  • average speed is measured in metres per second (m/s)
  • time is measured in seconds (s)

Example

A car travels 500 m in 50 s, then 1500 m in 75 s. Calculate its average speed for the whole journey.

First calculate total distance travelled:

500 + 1500 = 2000 m

Then calculate total time taken:

50 + 75 = 125 s

Then use the formula to calculate average speed:

average~speed = \frac{total~distance~travelled}{total~time~taken}

average speed = 2000 ÷ 125

average speed = 16 m/s

Calculating distance

The distance travelled by an object moving at an average speed can be calculated using the equation:

distance~travelled = average~speed~×~time

This is when:

  • distance travelled is measured in metres (m)
  • average speed is measured in metres per second (m/s)
  • time is measured in seconds (s)

Example

A motorbike travels at an average speed of 12 m/s for 25 s. Calculate the distance travelled in this time.

distance~travelled = average~speed~×~time

distance travelled = 12 × 25

distance travelled = 300 m

Converting between units

Sometimes calculations require a conversion from one set of units to another. A common example involves converting a speed from kilometres per hour (km/h) to metres per second (m/s).

Example

A truck is travelling at 72 km/h. Calculate its speed in m/s.

First, convert the distance from kilometres (km) to metres (m):

1 km = 1,000 m

This means that 72 km = 72,000 m

Then convert the time from hours (h) to seconds (s):

1 h = 3,600 s

Then, substitute the figures to obtain the final value in m/s:

Speed (m/s) = 72,000 ÷ 3,600

Speed = 20 m/s