Speed and Velocity

This section explains speed and velocity covering, distance and speed, displacement and the distance travelled formula. 

Distance and Speed

Distance

Distance is a scalar quantity that refers to how much ground an object has covered, regardless of the direction. It is measured in metres (m).

Speed

Speed is also a scalar quantity, and it measures how quickly an object moves, irrespective of direction. It is the rate at which distance is covered.

The formula to calculate speed is:

$$\text{Speed (v)} = \frac{\text{Distance (d)}}{\text{Time (t)}}$$ 

Where:

• v is the speed in metres per second (m/s).
• d is the distance travelled in metres (m).
• t is the time taken in seconds (s).

Example:

If a car travels 100 metres in 20 seconds, the speed is calculated as:

$$v = \frac{d}{t}$$

$$v = \frac{100 \, \text{m}}{20 \, \text{s}}$$

$$v = 5 \, \text{m/s}$$ 

So, the speed of the car is 5 m/s.

Displacement

Displacement is a vector quantity that refers to the straight-line distance from an object's starting point to its final position, along with the direction of travel. It differs from distance because displacement considers direction, whereas distance does not.

For example:

• If an object moves in a straight line, the distance travelled and the displacement are the same.
• If an object moves in a curved path, the distance travelled is greater than the displacement.

Displacement is measured in metres (m), and it can be positive or negative depending on the direction.

Distance Travelled Formula

To calculate the distance travelled, you can use the basic formula for speed, rearranged:

$$\text{Distance (d)} = \text{Speed (v)} \times \text{Time (t)}$$ 

Example:

If a runner is moving at a speed of 8 m/s for a time of 15 seconds, the distance travelled is:

$$d = v \times t$$

$$d = 8 \, \text{m/s} \times 15 \, \text{s}$$

$$d = 120 \, \text{m}$$

So, the distance travelled by the runner is 120 metres.

Velocity

Velocity is a vector quantity, which means it has both magnitude (speed) and direction. It is similar to speed but includes information about the direction of travel.

The formula for velocity is:

$$\text{Velocity (v)} = \frac{\text{Displacement (s)}}{\text{Time (t)}}$$ 

Where:

• v is the velocity in metres per second (m/s).
• s is the displacement in metres (m).
• t is the time in seconds (s).

Example:

If a person runs 200 metres to the north in 40 seconds, the velocity is:

$$v = \frac{s}{t}$$

$$v = \frac{200 \, \text{m} \, \text{north}}{40 \, \text{s}}$$

$$v = 5 \, \text{m/s north}$$

So, the velocity of the person is 5 m/s north.

Key Points:

• Distance is a scalar quantity that measures how much ground an object covers, while displacement is a vector quantity that includes both the distance and direction.
• Speed is the rate of distance covered, whereas velocity is the rate of displacement, including direction.
• The formulas for calculating distance, speed, and velocity are fundamental in understanding the motion of objects in GCSE Physics.