Speed, Distance and Time - Concept, Formulas & Questions

The reading material provided on this page for Speed, Distance and Time is specifically designed for students in grades 5 to 12. So, let's begin!

Introduction & Concept of Speed, Distance & Time

The concept of speed, time and distance holds significant importance in the mathematics section of various competitive exams. It is a fundamental topic that finds applications in different scenarios such as motion in a straight line, circular motion, boats and streams, races, clocks, and more. Understanding the interplay between speed, distance, and time is crucial for solving problems related to these areas. Aspirants should aim to grasp the relationship between these factors to excel in their exam preparation.

Speed

It can be defined as the rate at which an object covers distance. It represents how fast or slow an object is moving. Mathematically, speed is calculated by dividing the distance travelled by the time taken. The standard unit of speed is meters per second (m/s), although other units such as kilometres per hour (km/h) or miles per hour (mph) are commonly used in everyday situations.

Formula of Speed

Example: A train covers a distance of 240 km in 3 hours. What is the speed of the train?

Solution: Distance = 240 km
Time = 3 hours

Speed = Distance / Time
= 240/3
= 80 km/h

Average Speed

Average speed in mathematics refers to the overall rate at which an object or individual covers a certain distance over a specific period of time. It is determined by dividing the total distance travelled by the total time taken.

Formula of Average Speed

Example: A cyclist travels 60 kilometres at a speed of 30km/h hours and then continues for another 40 kilometres at a speed of 20 km/h. What is the cyclist's average speed for the entire journey?

Solution: To find the average speed, we need to determine the total distance travelled and the total time taken for the entire journey.

First, let's calculate the time taken for the first part of the journey:
Time is taken for the first part = Distance / Speed
= 60 km / 30 km/h
= 2 hours

Now, let's calculate the time taken for the second part of the journey:
Time is taken for the second part = Distance / Speed
= 40 km / 20 km/h
= 2 hours

To find the total time taken for the entire journey, we sum up the individual times:
Total time taken = 2 hours + 2 hours = 4 hours

Next, we calculate the total distance travelled:
Total distance = 60 km + 40 km = 100 km

Finally, we can determine the average speed:
Average speed = Total distance / Total time taken
= 100 km / 4 hours
= 25 km/h

Therefore, the cyclist's average speed for the entire journey is 25 km/h.

Time

It refers to the measurement of the duration of an event or the interval between two events. It is typically measured in units of seconds, minutes, hours, days, weeks, months, and years.

Formula of Time

Example: A man walks at a speed of 6 km/h and covers a distance of 24 km. How long does it take to cover the distance?

Solution: Speed = 6 km/h
Distance = 24 km
Time = Distance/Speed
= 24/6
= 4 hours

Distance

It refers to the measurement of the separation between two points in space. It is typically measured in units of meters, kilometres, miles, or feet. Distance can also refer to the amount of space covered by a moving object, such as the distance travelled by car or the distance covered by a runner in a race.

Formula of Distance

Example: A car is travelling at a speed of 60 km/h. How far will it travel in 3 hours?

Solution: Distance = 60 km/h x 3 hours
= 180 km

Relationship between Speed, Time and Distance

The relationship between speed, time, and distance can be described using the formula: