# Speed and Velocity

## Speed and Velocity

When an object is in motion the rate at which it covers distance is measured as its speed or velocity.

You may see speed written in Miles per Hour (mph), or Kilometers per Hour (kph), however, the SI unit is meters per second (m/s).

Speed requires no direction, only magnitude.

*Speed is a scalar.*

Velocity is also a quantity of a moving object, however, velocities have direction as well as magnitude. ** Velocity is a vector.** Like speed, the SI unit is also m/s.

**•** Speed is the scalar magnitude component of velocity.

**•** Velocity is speed in a stated direction.

(Tip: Many students confuse these two words in exams, think carefully when answering a question, do you need to mention direction? If so use velocity not speed. If you are not sure use velocity.)

All the units for measuring speed and velocity are very similar, they consist of a distance per unit of time.

Velocity and speed are a measure of the ** rate of change of distance with respect to time**. Or put another way, how far an object goes in how much time.

As speed is a scalar it can only ever have positive values, velocity as a vector can be either positive or negative. Like forces, the + or - indicates opposite directions.

When an object is moving in a circular path, its speed (magnitude of motion) may remain constant, but because the object is changing direction its velocity is also changing. [there is more on this in the section on circular motion].

## Calculating Speed

When we measure the time it takes for an object to cover a given distance, we can calculate the ** average speed**_ _of the object for that journey.

*Average Speed* = Distance travelled / time taken

or _ s =d /t _

Recall distances are in meter (m) and time is in seconds (s)

The unit of measurement of speed is, metersper second (m/sor ms^{-1})

Worked Example

A car travels along a stretch of motorway 1.5 Km long in 50 s. What is the average speed of the car?

*Average speed = distance / time*

_Average speed _= (1.5 x 1000) / 50 [distance must be in meters not Kilometers]

*Average speed* = 30 m/s

The equation can be rearranged to calculate the distance travelled.

*Distance travelled = speed x time*

Worked Example

A Boeing 747 has a cruising speed of 245 m/s on route to New York. If it travels at this speed for 6 hours, how far has the plane travelled?

Convert the time into seconds first: 6 hours x 3600 s= 21,600 s(2.16 x 10^{4} s)

*Distance = speed x time*

*Distance* = 245 x 21,600

*Distance = 5,292,000 m* or in standard form 5.292 x10^{6 }m

## Distance Time Graphs

A distance-time graph is a way of representing the journey of an object as a graph. From this, it is possible to describe the journey and use it to calculate the object’s speed.

Look at this example of a distance-time graph. What is happening to the object at each stage of its journey?

It begins at 0m/s at 0 s - so it is stationary, to begin with.

A: It travels a distance of 2 m in 20 seconds. As the line is straight this tells us it was moving at a constant speed.

B: The distance does not change for the next 10 seconds. This means the object is stationary.

C: The distance increase for the next 5 seconds. As the line is straight the object is moving at a constant speed. The line is steeper than at A, so the speed is greater.

D: As with B, the distance is not changing over time so the speed is zero.

Notice that__ the gradient of the line represents the speed of the object__.

**•** A - the gradient is 2 / 20 or 0.1 m/s.

**•** C - the gradient is 2 / 5 or 0.4 m/s

**•** B - the gradient is 0 or 0 m/s - the object is not moving.

What does a curved line mean?

Answer: The distance is increasing over time, so the object is moving. The rate of change is not constant, this indicates__ the object is accelerating__.

Note: If the curve bent in the other direction, the gradient was getting less, this would indicate the object was decelerating.

(Tip: In the exam, you might be asked about velocity-time graphs too. Be very careful; distance-time and velocity-time graphs look very similar. Double check which one you are looking at before you answer any questions. It takes only a second to do, but could save you making a big mistake.)

## Measuring Speed

Measuring the speed of an object in any situations requires the measurement of distance and of time. A standard set-up for this in a lab is shown in the diagram below.

There a number of ways to measure the speed, some are more accurate and reliable than others.

Method 1: The distance is measured with a meter-ruler and the time by using a stop-watch.

Advantages: Simple to set-up and easy to perform the experiment.

Disadvantages: Human reaction times to operate the stop-watch are variable and add a small margin of error to the measurements.

Method 2: The time can be measured using a computer and a device called a light gate.

As the trolley passes the first light gate it activates the timer, the second one stops the timer.

Most software will also then calculate the average speed of the trolley.

Advantages: Reliable and accurate measurement of time. The software can perform the calculation. This removes most of the human error and produces more accurate results.

Disadvantage: More expensive and time-consuming to set-up.

Method 3: Sonar sensors, linked to a data logger or computer can track the motion of the trolley in real time. These devices are similar to speed measuring signs you might see at the side of the road.

A typical example of a sonar data-capture device.

Advantages: Very accurate and very reliable. They can also provide data to software that will calculate speed and draw a distance-time graph.

Disadvantages: They are more expensive than some other methods and can take time to get them aimed at the moving object.

## Everyday Examples of Speed

Examples of the speed of typical objects

Object | Speed (m/s) | Speed (mph) |

Gentle breeze | 4 | 9 |

Gale | 12 | 27 |

Sound in air | 330 | 738 |

Sound in water | 1498 | 3350 |

Light (in a vacuum) | 300,000,000 | 671,080,887 |

Walking | 1.3 | 3 |

Car on motorway | 31 | 70 |

Express train | 58 | 130 |

Running | 3.6 | 8 |

Cycling | 5.4 | 12 |

The table above gives some examples of typical speeds of various objects. In an exam, the speeds in m/s would be used.The mph equivalents are only provided for your reference.

The speeds for walking, cycling and running are those on an average adult. You will also see speeds for different objects given in various other units. In Europe, speeds are given in Kilometers per hour (kph) for example.Wind speeds can be in mph or sometime in Knots. A knot is also a unit of speed used for aeroplanes and ships.

Remember, however, that in science we use the standard m/s for all speeds.

One very important speed in physics is the speed of light in a vacuum. This is a constant and never changes.In physics, it has the symbol c, as in the equation E=mc^{2}.

**The speed of light is the fastest speed possible, nothing goes faster than light.**

- What is the difference between speed and velocity?
- Your answer should include: scalar / vector

Explanation:*Speed is a scalar and only has magnitude. Velocity is a vector and has both magnitude and direction.* - A train travels from London to Manchester in 2 hours 10 minutes. It is 320 Km from London to Manchester. What was the average speed of the train in m/s (to 4 s.f.)?
- Your answer should include: 41.03 / 41.03m/s

Explanation:*Distance: 320 km x 1000 = 320,000m Time: 2 hours x 3600 s + 10 minutes x 60 s = 7200 s Speed = distance / time 3200,000 / 7200 = 41.03 m/s* - Explain why using a light gate to measure speeds in an experiment is better than using a stop-clock and ruler.
- Your answer should include: accurate / human error

Explanation:*The light gate is more accurate as there is no human error as there would be with a stop-clock.*