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1.2.1 Speed and velocity

Speed: the distance covered every second

Definition

Speed

The distance travelled per unit time.

v=st v = \frac{s}{t} v=ts​

where vvv is the speed in m/s\text{m/s}m/s, sss is the distance in m\text{m}m and ttt is the time in s\text{s}s.

  1. A speed of 8 m/s8\ \text{m/s}8 m/s means 8 m8\ \text{m}8 m is covered in every second; "how fast it goes" describes speed but does not define it.
  2. Rearrange the same equation as the question needs: s=v×ts = v \times ts=v×t for a distance, t=s/vt = s/vt=s/v for a time.
  3. The SI unit is m/s\text{m/s}m/s, but km/h\text{km/h}km/h and cm/s\text{cm/s}cm/s are also used.
  4. Keep the units consistent: whatever units go in set the unit that comes out, so a distance in km\text{km}km with a time in h\text{h}h gives a speed in km/h\text{km/h}km/h.
  5. Convert with 1 km=1000 m1\ \text{km} = 1000\ \text{m}1 km=1000 m and 1 h=3600 s1\ \text{h} = 3600\ \text{s}1 h=3600 s, which together give 1 m/s=3.6 km/h1\ \text{m/s} = 3.6\ \text{km/h}1 m/s=3.6 km/h.

Velocity: speed with a direction attached

Definition

Velocity

Speed in a given direction.

  1. A velocity is only fully stated with a direction: 8.0 m/s8.0\ \text{m/s}8.0 m/s due north, or 12 m/s12\ \text{m/s}12 m/s downwards; a speed needs only a number and a unit.
  2. The same equation v=s/tv = s/tv=s/t gives the velocity when an object moves in a straight line in one fixed direction.
  3. An object can travel at constant speed while its velocity changes, because a change of direction alone changes the velocity.
  4. A car going round a roundabout at a steady 8.0 m/s8.0\ \text{m/s}8.0 m/s keeps its speed but has a continuously changing velocity, since the direction it heads in changes every instant.

Average speed: total distance over total time

Definition

Average speed

average speed=total distance travelledtotal time taken \text{average speed} = \frac{\text{total distance travelled}}{\text{total time taken}} average speed=total time takentotal distance travelled​
  1. Real journeys are not steady: a bus speeds up, slows down and stops.
  2. A single value of v=s/tv = s/tv=s/t across the whole trip is only the average speed, the steady speed that would cover the same distance in the same time.
  3. That is different from the instantaneous speed, the speed at one moment, which is what a speedometer shows.
  4. The marks live in the word total: the total time includes every part of the journey, including any time spent stationary at lights or in a queue.
Common Mistake
  • Constant speed does not mean constant velocity. An object turning a corner keeps its speed but changes its velocity, because its direction changes.
  • Do not average the speeds. Adding two speeds and halving only works if the two stages take exactly the same time; always go back to total distance over total time.
  • Do not drop stationary time from the total time; a stop still lasts, and it drags the average speed down.
  • Do not mix units inside one substitution: convert km\text{km}km to m\text{m}m and hours or minutes to seconds before substituting if the answer is wanted in m/s\text{m/s}m/s.
Exam technique
  • Write the equation from recall before substituting; marks are staged, so a correct equation and substitution still score even if the arithmetic slips, and the final answer needs its unit.
  • Match the command word: "define speed" needs the wording distance travelled per unit time; "state the velocity" needs a number, a unit and a direction.
  • The word average signals that the motion was not steady, so use total distance over total time, not one stage.
  • If the data is in km\text{km}km and h\text{h}h but the answer is wanted in m/s\text{m/s}m/s, convert first and show the conversion.
Self review
  • Define speed, and give the equation with its unit.
  • What extra information does a velocity carry that a speed does not?
  • How can an object have a constant speed but a changing velocity?
  • How do you find the average speed for a journey that includes a stop?
  • Convert 20 m/s20\ \text{m/s}20 m/s into km/h\text{km/h}km/h.
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1.2.1 Speed and velocity Revision Guide

  1. IGCSE
  2. /Physics
  3. /1.2.1 Speed and velocity

Revision notes for CIE IGCSE Physics 1.2.1 Speed and velocity: explanations and worked examples.

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