GCSE Physics - Speed, Velocity, Distance & Displacement | Scalar & Vector Quantities (2026/27 exams)

Transcript

In today's video, we're going to look at the terms speed and velocity and see how we can calculate each of them. As you saw in a previous video, quantities can be of two types, scalar or vector. Scalar quantities only have a magnitude which is the size or extent of something whereas vector quantities have both a magnitude and a direction. So speed would be considered a scalar quantity because it only conveys magnitude. This might be a person running at 4 m/s or a plane flying at 250 m/s.

Velocity on the other hand is a vector because it also has direction like a person cycling 6 m/s east or a train traveling backwards at 55 m/s. It's really common in the exams to get speed and velocity confused. So just make sure you're completely sure about which one's which and try not to get them mixed up. Another pair of quantities you need to know are distance and displacement. Distance is a scalar as it only gives magnitude like 10 m or 40 m.

Displacement though is a vector as it has direction as well. For example, a person running 40 m east or a ball that falls 2 m downwards. To help us understand this difference, let's imagine that we have a train traveling across a bridge. The bridge is 550 m long and it takes the train 10 seconds to cross it. To calculate the speed of the train, we need to take the distance it traveled and divide it by the time that it took.

So 550 m over 10 seconds which gives us the scalar quantity of 55 m/s. If we took this same equation but replace the scalar quantity of distance traveled with the vector quantity of displacement, we' then be able to get the vector quantity of velocity. If we knew the direction that the train was traveling in, for example, east, then instead of writing the distance, we could write the displacement, which would be 550 m east. The time would still be 10 seconds, and the velocity would still have a value of 55, but the units of the velocity would be meters/s east rather than just meters/s like we got for speed. Now, the symbol formulas for these two equations can be kind of confusing because they use the letter S to represent different things.

For velocity, the S refers to the displacement. But in the speed equation, the S stands for speed and the D is distance. In both cases though, the T stands for time. In reality, people often use the velocity equation regardless of whether they've actually got a direction or not. The benefit of using velocity is that you can have a negative velocity to represent going backwards.

Now, often objects don't actually move at a constant speed, but instead vary along their journey. We can still use this equation, but we need to divide the total distance or displacement by the total time that the journey took. And the value that we calculate will then be the average speed or average velocity. To give you an idea of real life speeds in meters/s, people walk at about 1.5 m/s, run at around 3 m/s, and cycle about 6 m/s. All of these numbers do of course vary a lot though depending on the age and health of the individual and how much effort they're putting in at the time.

Then for vehicles, a car on the main road might travel around 25 m/s, while a fast train could travel 55 m/s, and planes can exceed 250 m/s. It's not only the speed of objects that varies, though. As we'll see in a later video, sound waves travel at 330 m per second when they're in air, which is a figure that you need to remember. But when they're traveling through different mediums like water, their speed changes. A more relatable example is the wind, which is just the natural movement of air.

This can vary from almost 0 m/s on a still day to faster than a speeding train on a windy day and can be affected by things like temperature, atmospheric pressure, and these structures is traveling past like buildings or mountains. If you haven't heard yet, you can find all of our videos on our website, cognito.org. You'll also find questions, flashcards, exam style questions, and pass papers. And we track all of your progress so that you always know what to study next. So sign up for free by clicking here or browse our playlist here on YouTube.