Hello, and welcome to today's mathematics lesson! We are going to explore a fascinating chapter — the Idea of Speed, Distance, and Time. These three quantities are everywhere around us. When you walk to school, when a train rushes past, or when a bird flies across the sky — speed, distance, and time are always at play. By the end of this lesson, you will understand how these three are connected, how to calculate each one, and how to solve real-life problems involving moving objects.
Let us begin with the most fundamental concept — speed.
Speed of a body is the distance covered by the body in unit time. This is our precise definition. Think of it this way — speed tells us how fast something is moving. The faster an object moves, the more distance it covers in the same amount of time.
From this definition, we get our three essential formulas.
First, speed equals distance divided by time. We write this as: Speed = Distance/Time.
From this, we can rearrange to find the other two quantities. Distance equals speed multiplied by time: Distance = Speed × Time. And time equals distance divided by speed: Time = Distance/Speed.
Now, units matter tremendously in these calculations. When distance is measured in metres and time in seconds, speed comes out in metres per second, written as m s⁻¹. When distance is in kilometres and time in hours, speed is in kilometres per hour, written as km h⁻¹. The golden rule is this — your units must always match. If speed is in metres per second, time must be in seconds. If speed is in kilometres per hour, distance must be in kilometres.
Very often, we need to convert speed from one unit to another. Let me show you the clever method for this.
To convert kilometres per hour to metres per second, we multiply by 5/18. To convert metres per second to kilometres per hour, we multiply by 18/5.
Why does this work? Let us see. One kilometre per hour means one kilometre in one hour. One kilometre equals one thousand metres. One hour equals sixty minutes, and each minute has sixty seconds — so one hour is three thousand six hundred seconds. Therefore, 1 km h⁻¹ = 1000 m / 3600 s, which simplifies to 5/18 m s⁻¹. This is the reasoning behind our conversion factors.
Let us work through an example together. Suppose we want to convert ninety kilometres per hour into metres per second. We take ninety and multiply by 5/18. Ninety divided by eighteen is five, and five times five gives us twenty-five. So ninety kilometres per hour equals twenty-five metres per second.
Here is another situation. A boy covers one point two kilometres in forty minutes. We want his speed in kilometres per hour. First, we convert forty minutes to hours — that is forty over sixty, which simplifies to two-thirds of an hour. Now speed equals distance over time, so we have one point two divided by two-thirds. Dividing by a fraction means multiplying by its reciprocal, so one point two times three halves. This gives us one point eight kilometres per hour.
For metres per second, we convert one point two kilometres to one thousand two hundred metres, and forty minutes to forty times sixty seconds, which is two thousand four hundred seconds. Speed equals one thousand two hundred over two thousand four hundred, which is one-half or zero point five metres per second.
Now let us distinguish between two important types of speed — uniform and variable.
If a body covers equal distances in equal intervals of time, its speed is said to be uniform. Otherwise, its speed is variable.
Imagine a car travelling on a highway. If it covers sixty kilometres in the first hour, another sixty in the second hour, and another sixty in the third hour — its speed is uniform. The speedometer would show a steady reading throughout.
But if the same car covers sixty kilometres in the first hour, sixty-seven in the second, and fifty-eight in the third — the speed is variable. Even if the distances were equal but the times different — say first sixty kilometres in one hour, second sixty kilometres in one hour twenty minutes, third sixty kilometres in one hour thirty minutes — the speed would still be variable because the time intervals are not equal.
When speed varies, we often talk about average speed. Average speed equals total distance covered divided by total time taken. This gives us a single value that represents the overall journey, even if the actual speed kept changing.
Consider a train that covers first one hundred twenty kilometres in two hours, next one hundred sixty kilometres in three hours, and last one hundred forty kilometres again in two hours. The total distance is four hundred twenty kilometres. The total time is seven hours. So the average speed is four hundred twenty divided by seven, which equals sixty kilometres per hour.
Here is a slightly more involved example. A man covers sixty kilometres at thirty kilometres per hour, and then fifty kilometres at twenty kilometres per hour. For the first part, time equals sixty over thirty, which is two hours. For the second part, time equals fifty over twenty, which is two and a half hours. The total time is four and a half hours. The total distance is one hundred ten kilometres. Therefore, average speed equals one hundred ten divided by four and a half, which is one hundred ten times two over nine, giving us twenty-four and four ninths kilometres per hour.
Let us now explore a special and practical application — moving trains.
When a train passes a stationary object like a pole or a person standing still, the distance the train must cover equals its own length. The train has moved completely past only when its last carriage clears the object.
But when a train passes a platform, the situation changes. Now the train must cover not just its own length, but also the length of the platform. The distance becomes: length of train plus length of platform.
Let us see this in action. A train one hundred sixty metres long travels at seventy-two kilometres per hour. First, we convert this speed to metres per second: seventy-two times 5/18 equals twenty metres per second.
To pass a telegraph post, the train covers one hundred sixty metres at twenty metres per second. Time equals one hundred sixty over twenty, which is eight seconds.
To pass a two hundred metre platform, the distance becomes one hundred sixty plus two hundred, which is three hundred sixty metres. Time equals three hundred sixty over twenty, which is eighteen seconds. Notice how the platform nearly triples the time needed!
Finally, let us consider two runners starting from the same point. If they run in the same direction, the distance between them after any time equals the difference of the distances each has covered. The faster runner pulls ahead. If they run in opposite directions, the distance between them equals the sum of the distances covered — they are moving apart from each other. With speeds of eight and eleven kilometres per hour, after two hours in the same direction they are six kilometres apart — that is, twenty-two minus sixteen. In opposite directions, they would be thirty-eight kilometres apart — that is, sixteen plus twenty-two.
Let us recap the key takeaways from today's lesson.
First, speed is defined as distance covered in unit time. This gives us three fundamental formulas: speed equals distance divided by time, distance equals speed multiplied by time, and time equals distance divided by speed.
Second, units must always be consistent — metres with seconds for metres per second, kilometres with hours for kilometres per hour.
Third, to convert kilometres per hour to metres per second, multiply by 5/18; to convert metres per second to kilometres per hour, multiply by 18/5.
Fourth, uniform speed means equal distances in equal time intervals; otherwise speed is variable, and we use average speed — total distance over total time — to describe the overall motion.
Fifth, when a train passes a stationary object, distance equals train length; when passing a platform, distance equals train length plus platform length.
And sixth, for two bodies moving from the same point, distance between them after a given time equals the difference of distances covered when moving in the same direction, and the sum of distances covered when moving in opposite directions.
Speed, distance, and time are woven into every journey you take. Whether you are estimating when to leave for school, watching vehicles pass by, or simply curious about how fast things move — these concepts empower you to understand and calculate motion. Keep practising with real examples around you, and these ideas will become second nature.
Thank you for your attention, and happy learning!