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P5 I) Speed, Distance & Time
P5 I) Speed, Distance & Time
There are two different quantities in science; scalar and vector quantities. Scalar quantities just have magnitude (size), and vector quantities have both magnitude (size) and direction. A few examples of scalar quantities are speed, distance, energy, mass and temperature. A few examples of vector quantities are velocity, displacement, force and weight.
We are going to have a look at distance, displacement, speed and velocity in a bit more detail in this section.
We are going to have a look at distance, displacement, speed and velocity in a bit more detail in this section.
Distance & Displacement
Distance measures how far an object has moved. An example is 40 kilometres (km). This is a scalar quantity because we are only given the magnitude (40 km) and not the direction; has the object moved 40 km in a northwards direction? Has the object moved 40 km upwards? Etc.
Displacement is a vector quantity as it gives us both magnitude and direction (the direction for displacement is measured in a straight line from the starting point to the finishing point). For example, a plane travelled 40 km at a bearing of 125°. The magnitude for this is 40 km and the direction is a bearing of 125°.
When we are carrying out scientific investigations, it is sometimes useful to know what the scalar and vector quantities are. This is because sometimes a vector quantity will not tell you the full picture. For example, if we walk 10 metres in an eastwards direction and then turn around and walk 10 metres in a westwards direction, we would end up back at the starting point. The displacement for these two movements would be 0 metres because we have ended up at the same point that we started at. However, the distance travelled would be 20 metres (10 m in an eastwards direction and 10 m in a westwards direction; 10 + 10 = 20 m).
Distance measures how far an object has moved. An example is 40 kilometres (km). This is a scalar quantity because we are only given the magnitude (40 km) and not the direction; has the object moved 40 km in a northwards direction? Has the object moved 40 km upwards? Etc.
Displacement is a vector quantity as it gives us both magnitude and direction (the direction for displacement is measured in a straight line from the starting point to the finishing point). For example, a plane travelled 40 km at a bearing of 125°. The magnitude for this is 40 km and the direction is a bearing of 125°.
When we are carrying out scientific investigations, it is sometimes useful to know what the scalar and vector quantities are. This is because sometimes a vector quantity will not tell you the full picture. For example, if we walk 10 metres in an eastwards direction and then turn around and walk 10 metres in a westwards direction, we would end up back at the starting point. The displacement for these two movements would be 0 metres because we have ended up at the same point that we started at. However, the distance travelled would be 20 metres (10 m in an eastwards direction and 10 m in a westwards direction; 10 + 10 = 20 m).
Speed & Velocity
Speed is how fast something is travelling. Speed is a scalar quantity as we are given magnitude (size) and no direction. An example is 5 metres per second (m/s).
Velocity is a vector quantity as we are given both magnitude and direction. An example is 5 metres per second (m/s) north.
If an object is travelling at a constant speed and changes direction, it will result in the velocity of the object changing. For example, if we had an object travelling around in a circle, the direction of travel for the object will be constantly changing, which means that the velocity of the object will also be constantly changing. An example of this happening is a car going around a roundabout or a planet orbiting a star (the earth orbiting the sun).
Speed is how fast something is travelling. Speed is a scalar quantity as we are given magnitude (size) and no direction. An example is 5 metres per second (m/s).
Velocity is a vector quantity as we are given both magnitude and direction. An example is 5 metres per second (m/s) north.
If an object is travelling at a constant speed and changes direction, it will result in the velocity of the object changing. For example, if we had an object travelling around in a circle, the direction of travel for the object will be constantly changing, which means that the velocity of the object will also be constantly changing. An example of this happening is a car going around a roundabout or a planet orbiting a star (the earth orbiting the sun).
Speed, Distance & Time
The equation that links speed, distance and time is shown below.
The equation that links speed, distance and time is shown below.
It is usually the case that the speed of an object is constantly changing, and this is why speed is usually average speed (mean speed).
I am going to use the formula above for the following examples, but sometimes the formula can be written differently with s as the distance and v as the speed. This formula is shown below.
I am going to use the formula above for the following examples, but sometimes the formula can be written differently with s as the distance and v as the speed. This formula is shown below.
Let’s now have a few examples.
Example 1
A man runs 75 metres in 25 seconds. Work out the average speed for the runner.
The question is asking us to find average speed, so we cover up speed in the formula triangle. When we do this, we see that we find speed by dividing the distance by the time.
A man runs 75 metres in 25 seconds. Work out the average speed for the runner.
The question is asking us to find average speed, so we cover up speed in the formula triangle. When we do this, we see that we find speed by dividing the distance by the time.
We now sub the values in. The question tells us that the distance is 75 metres and the time is 25 seconds; we sub these values in.
The average speed of the runner is 3 m/s.
Example 2
A car is travelling at an average speed of 25 m/s for 50 seconds. Work out the distance travelled by the car in these 50 seconds. Give your answer in kilometres.
The question is asking us to find the distance travelled, so we cover up distance in the formula triangle. When we do this, we see that we find the distance by multiplying the average speed by the time.
A car is travelling at an average speed of 25 m/s for 50 seconds. Work out the distance travelled by the car in these 50 seconds. Give your answer in kilometres.
The question is asking us to find the distance travelled, so we cover up distance in the formula triangle. When we do this, we see that we find the distance by multiplying the average speed by the time.
The question tells us that the average speed is 25 m/s and the time is 50 seconds; we sub these values into the calculation.
The distance travelled during these 50 seconds is 1,250 metres. The question asks us to give the distance travelled in kilometres. There are 1,000 metres in a kilometre, which means that we convert metres to kilometres by dividing by 1000.
The distance travelled in kilometres is 1.25 km.
Typical Speeds
You are required to know some typical speeds of some activities and vehicles. These typical speeds are shown below:
All of the values above will vary depending on a variety of different factors. For example, the speeds for walking, running and cycling will vary on fitness, age, terrain (pavement, uneven fields, up a hill) and distance travelled.
The typical speed of sound through air is 330 m/s. However, the speed of sound varies depending on what the sound waves are travelling through.
The speed of wind also varies. Some days it is extremely windy and other days there is no wind at all. The speed of wind is affected by temperature, atmospheric pressure and the surroundings (such as buildings, forests, mountains etc.).
You are required to know some typical speeds of some activities and vehicles. These typical speeds are shown below:
- An individual walking – 1.5 m/s
- An individual running – 3 m/s
- An individual cycling – 6 m/s
- A car – 25 m/s
- A train – 30 m/s
- An aeroplane – 250 m/s
All of the values above will vary depending on a variety of different factors. For example, the speeds for walking, running and cycling will vary on fitness, age, terrain (pavement, uneven fields, up a hill) and distance travelled.
The typical speed of sound through air is 330 m/s. However, the speed of sound varies depending on what the sound waves are travelling through.
The speed of wind also varies. Some days it is extremely windy and other days there is no wind at all. The speed of wind is affected by temperature, atmospheric pressure and the surroundings (such as buildings, forests, mountains etc.).