chevron_left Speed: Distance travelled by object in given time chevron_right

Speed: The Measure of Motion

The Core Definition and Formula of Speed

At its simplest, speed answers the question: "How fast is it going?" It is a scalar quantity^[1], meaning it only has magnitude (a numerical value) and no specific direction. The mathematical definition of speed is straightforward and is one of the first formulas students encounter in physics.

Let's consider a simple example. If a bicycle travels a distance of 300 meters in a time of 60 seconds, its speed is calculated as follows:

$Speed = \frac{300 \text{ m}}{60 \text{ s}} = 5 \text{ m/s}$

This means the bicycle covers 5 meters every second. The units of speed are always a unit of distance divided by a unit of time. Common units include meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph).

Average Speed vs. Instantaneous Speed

It is rare for an object to move at a perfectly constant speed. A car on a trip will speed up, slow down, and even stop. This leads to two important ways of thinking about speed.

Average Speed is the total distance travelled divided by the total time taken for the entire journey. It gives you an overall picture of the motion.

Example: A family goes on a road trip. They travel 240 kilometers in 3 hours. Their average speed is:

$Average Speed = \frac{240 \text{ km}}{3 \text{ h}} = 80 \text{ km/h}$

This doesn't mean they were driving at exactly 80 km/h the whole time. They might have been faster on the highway and slower in the city, but on average, they covered 80 km each hour.

Instantaneous Speed is the speed of an object at a specific moment in time. This is the value you see on a car's speedometer. It tells you how fast you are going right now.

Speed and Velocity: A Critical Distinction

While often used interchangeably in everyday language, speed and velocity have distinct scientific meanings. As mentioned, speed is a scalar quantity. Velocity, on the other hand, is a vector quantity^[2]. This means velocity includes both magnitude (speed) and direction.

For example, if a car is travelling north at 60 km/h, its velocity is 60 km/h north. If it turns around and travels south at 60 km/h, its speed is still 60 km/h, but its velocity is now 60 km/h south. A change in direction, even if the speed remains the same, means a change in velocity.

Calculating Speed in Real-World Scenarios

Let's apply our knowledge to solve practical problems. Using the formula $Distance = Speed \times Time$ is a common task.

Scenario 1: Planning a Journey
How far can an airplane fly if it travels at an average speed of 800 km/h for 5.5 hours?

$Distance = 800 \text{ km/h} \times 5.5 \text{ h} = 4,400 \text{ km}$

Scenario 2: Comparing Runners
Two runners complete a 100-meter race. Runner A finishes in 12.5 seconds. Runner B finishes in 11.9 seconds. Who is faster, and what are their average speeds?

• Runner A: $Speed = \frac{100 \text{ m}}{12.5 \text{ s}} = 8 \text{ m/s}$
• Runner B: $Speed = \frac{100 \text{ m}}{11.9 \text{ s}} \approx 8.4 \text{ m/s}$

Runner B has a higher average speed and is therefore faster.

Common Mistakes and Important Questions

Footnote

^[1] Scalar Quantity: A physical quantity that is described solely by its magnitude (size or number). Examples include speed, distance, mass, and temperature.

^[2] Vector Quantity: A physical quantity that has both magnitude and direction. Examples include velocity, force, displacement, and acceleration.