Forces - 5.6.1.2 Speed (GCSE Physics AQA)

Speed

Speed of Objects

• Speed is a scalar quantity. Like distance, speed is also a scalar quantity. The speed of an object will tell us how fast it is moving, but will not tell us the direction of movement.
• Speed is not constant. The speed of an object is not the same at all times (i.e. it is not constant). We can understand this fact because when we run or walk, we hardly ever travel at the exact same speed all the time.

The Speed of Wind and Sound

Speed of Sound

The speed of sound in air is usually 330m/s.

Although the standard speed of sound in air is 330m/s, it can vary. These changes in speed occur when sound waves pass through objects of different densities. The more dense the object, the slower the sound will travel.

Speed of Wind

Similarly, the speed of wind can also vary. When wind passes over or around certain objects, such as trees, it can experience some friction. This friction will lead to turbulence in the air, which in turn changes the speed of the wind. The temperature and the pressure of the air can also affect wind speed.

AQA Specification: Typical values may be taken as walking 1.5 m/s, running 3 m/s, cycling 6 m/s.

Speeds of Activity

For AQA exams, we need to know a few ‘typical’ values for different everyday activities and transport values.

Factors Affecting Speed

In the table, we have just seen the typical values for walking, running and cycling. The key thing to remember is that these were only ‘typical’ values – they can change due to 4 different factors:

• Age – as we get older, our fitness levels will decrease and we find it harder to run at the same speed as we did before.
• Terrain – a rough terrain will have more friction, reducing speed. Similarly, if the incline is higher, it takes more energy to run at the same pace.
• Distance travelled – as distances increase, our muscles get tired and lactic acid builds up due to anaerobic respiration. This leads to muscle cramps, and we find it harder to run as fast.
• Fitness – the more fit you are, the better you are able to cope with intense exercise. This is especially true for running.

Calculating Speed

Formula for Speed, Distance, Time

Where:

• distance, s, in metres, m
• Speed, v, in metres per second, m/s
• time, t, in seconds, s

In the exam, they will often give you two elements of a three part formula, and ask you to work out the third.

Question: Sophia is driving down a long road. It takes her 3 minutes to travel 4.5km. Calculate the speed at which she is driving, giving your answer with units.

1. Get the correct units.
Before we start to tackle the question, we need to check that we are in the right units.

3 minutes = 180 seconds
4.5 km = 4500 metres

2. Rearrange the equation.
In order to use our equation, we must rearrange it to give speed as the subject.

s = vt
v = s/t

3. Put in the numbers.
Now we can substitute in the values that we are given in the question and give the speed in m/s.

v = 4500 / 180
v = 25 m/s

Question: Jack runs the London Marathon in 4 hours and 20 minutes. The Marathon is 41.4 km long. Calculate his speed in metres per minute. (4 hours 20 minutes is equivalent to 4.333 hours as 20 minutes is 1/3 of an hour).

Method 1: Converting units at the end

Speed = Distance / Time = 41.4 / 4.333 = 9.56 km / h

You need to multiply by 1000 to convert into metres = 9554 m / h

You need to divide by 60 to convert to minutes = 159 m / min

The answer is therefore C, 159m.

Method 2: Converting units at the start

Speed = Distance / Time = (41.4 x 1000) / (4.33 x 60) = 159 m / min

The answer is therefore C, 159m.

Question: The graph below shows the velocities of three different bikers on a 3 hour journey.

i) What was the difference between the distance covered by Bike 3 and Bike 1?

Speed = Distance / Time
Distance = Speed x Time = Area under graph

The average velocity for Bike 1 is 50 km/h.

The average velocity for Bike 3 can be calculated by doing (60 + 0) / 2 = 30 km/h. This only works because Bike 3 has a straight line – it is not possible to do this for Bike 2.

Distance Bike 1 = 50 x 3 = 150 km
Distance Bike 3 = 30 x 3 = 90 km
The difference is 60km

ii) What is the distance covered by Bike 2?

Bike 2 does not have a straight line, so you have to work out the distance under the line segment by segment.

Area of Triangle = base x height x 1/2
Area of Square = length x width

Triangle 1 = 1 x 120 x 0.5 = 60
Triangle 2 = 1 x 20 x 0.5 = 10
Triangle 3 = 1 x 60 x 0.5 = 30

Square 4 = 1 x 100 = 100
Square 5 = 1 x 100 = 100

Area under graph = 60 + 10 + 30 + 100 + 100 = 300km = C

iii) What is the average speed of Bike 2?

You can work out average speed by working out the gradient. However, the line is not straight, so instead you can calculate a gradient (= speed) for each hour, and then work out an average.

• For the first hour the bike travels at 60 km/h average: (120 + 0) / 2.

• For the second hour the bike travels at 110 km/h average: (120 + 100) / 2

• For the third hour the bike travels at 130 km/h average: (100 + 160) / 2

Average of journey = (60 + 110 + 130) / 3 = 100 km/h = D

Non-Uniform Motion

For AQA exams, we need to be able to calculate the average speed of an object with non uniform motion.

In these types of questions, we can still apply the formula that we have just learnt; s = vt. The only difference is that we have to calculate the total distance and time, as shown in the following example.

Question: Josh is going on a bike ride. He starts off on a well-paved road, where he cycles 500m in 70s. He then comes to an uphill stretch, where he cycles a distance of 450m in 95 seconds. Calculate his average speed in m/ s and give your answer to 1dp.

1. Calculate the total time taken for the journey.
In this case, we need to add up

70 and 95.
70 + 95 = 165 seconds
839

2. Calculate the total distance travelled.

Again, we just have to add up 500 and 450.
500 + 450 = 950 metres

3. Use the formula.
We know that s = vt, but for this question we need to rearrange to find the speed.

s = vt
v = s/t
v = 950 / 165
v = 5.757575… m/s
v = 5.8 m/s (1dp)