3.2 Speed

Definition

Speed is the rate at which an object covers distance.

It describes how fast an object moves, without specifying the direction of motion.

An object moving at a greater speed covers more distance in the same amount of time, or covers the same distance in less time.

Since speed has magnitude but no direction, it is a scalar quantity.

SI Unit

The SI unit of speed is the meter per second (m/s).

A speed of 5 m/s, for example, means that an object travels 5 meters of distance each second.

Other units, such as kilometers per hour (km/h), are also commonly used.

Calculating Speed

For motion at constant speed, speed is calculated by dividing the distance travelled by the time taken.

v=dΔtv=\frac{d}{\Delta t}

v:v\,:speed
d:d\,: distance travelled
Δt:\Delta t\,: time taken

The equation can also be rearranged to calculate distance or time:

d=vΔtd=v\Delta t

Δt=dv\Delta t=\frac{d}{v}

Example 1

A car travels 150 m along a road in 10 s at constant speed.

Figure 3.2.1. A car travelling 150 m in 10 s at constant speed.

Its speed is

v=150m10sv=\frac{150\,\mathrm{m}}{10\,\mathrm{s}}

v=15m/sv=15\,\mathrm{m/s}

The car therefore travels 15 meters each second.

Average Speed

The speed of an object does not have to remain constant during a journey. An object may speed up, slow down, stop, or move at different speeds during different parts of its motion.

The average speed for the entire journey is defined as the total distance travelled divided by the total time taken.

vavg=dtotalΔttotalv_{\mathrm{avg}}=\frac{d_{\mathrm{total}}}{\Delta t_{\mathrm{total}}}

Average speed describes the overall rate at which distance is covered. It does not describe the speed at every moment during the motion.

Example 2

A cyclist travels 300 m in 20 s and then another 200 m in 20 s. The total distance travelled is

dtotal=300m+200m=500md_{\mathrm{total}}=300\,\mathrm{m}+200\,\mathrm{m}=500\,\mathrm{m}

The total time taken is

Δttotal=20s+20s=40s\Delta t_{\mathrm{total}}=20\,\mathrm{s}+20\,\mathrm{s}=40\,\mathrm{s}

Therefore,

vavg=500m40sv_{\mathrm{avg}}=\frac{500\,\mathrm{m}}{40\,\mathrm{s}}

vavg=12.5m/sv_{\mathrm{avg}}=12.5\,\mathrm{m/s}

The cyclist’s average speed for the entire journey is 12.5 m/s.

The average speed is calculated from the total distance and total time, rather than by considering only one part of the journey.

Average Speed on a Round Trip

Because speed is based on distance travelled, returning to the starting position does not make the average speed zero.

Figure 3.2.2. A runner completing a 400 m lap in 50 s.

For the motion shown in Figure 3.2.2, the total distance travelled is 400 m and the total time is 50 s.

Therefore,

vavg=400m50sv_{\mathrm{avg}}=\frac{400\,\mathrm{m}}{50\,\mathrm{s}}

vavg=8.0m/sv_{\mathrm{avg}}=8.0\,\mathrm{m/s}

Although the runner returns to the starting position, a distance of 400 m has been travelled. The average speed is therefore 8.0 m/s.

Instantaneous Speed

When the speed of an object changes, its instantaneous speed is its speed at a particular moment in time.

For example, the reading shown by a car’s speedometer gives the car’s instantaneous speed at that moment.

Average speed describes motion over a time interval, whereas instantaneous speed describes how fast an object is moving at a particular instant.

Figure 3.2.3. A speedometer showing the instantaneous speed of a car.

Key Points

  • Speed describes how fast an object moves.
  • Speed is the rate at which distance is travelled.
  • Speed is a scalar quantity.
  • The SI unit of speed is the meter per second (m/s).
  • For constant speed, v=dΔtv=\frac{d}{\Delta t}
  • Average speed is total distance travelled divided by total time taken.
  • Instantaneous speed is the speed of an object at a particular moment.
  • Average speed can be non-zero even when an object returns to its starting position.

← 3.1 Motion   

3.3 Velocity →