Class 6 Exam > Class 6 Notes > Mathematics Class 6 ICSE > Chapter Notes: Speed, Distance, and Time
Speed, Distance, and Time Chapter Notes | Mathematics Class 6 ICSE PDF Download
| Table of contents |
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| Introduction |
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| Speed |
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| Units of Speed |
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| Conversion of Units of Speed |
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| Solved Examples |
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Introduction
Imagine you're on a thrilling bike ride, zooming through the streets, or watching a speedy train whiz by! How fast are you going? How far will you travel? How long will it take? These exciting questions are answered by understanding speed, distance, and time. This chapter is like a roadmap to help you figure out how these three ideas work together. Whether it's a car racing down the highway or an athlete sprinting on a track, you'll learn how to calculate their speed, the distance they cover, or the time they take. Get ready to dive into a fun and practical world of motion!
Speed
- Speed is how fast an object moves, measured by the distance it covers in a specific amount of time.
- It tells us how quickly or slowly something travels from one place to another.
- Formula: Speed = Distance ÷ Time
- From this, we can derive:
- Distance = Speed × Time
- Time = Distance ÷ Speed
- If an object covers the same distance in equal time intervals, its speed is uniform.
- If the distances covered in equal time intervals vary, the speed is variable.
Example: A motorbike travels 120 km in 2 hours.
Step-by-step:
Step-by-step:
- Use the formula: Speed = Distance ÷ Time
- Distance = 120 km, Time = 2 hours
- Speed = 120 km ÷ 2 hours = 60 km/h
- So, the motorbike's speed is 60 km/h.
Units of Speed
- Speed is expressed in units based on distance and time.
- When distance is in kilometres (km) and time is in hours (h), speed is in kilometres per hour (km/h).
- When distance is in meters (m) and time is in seconds (s), speed is in meters per second (m/s).
Example: A car covers 33 km in 30 minutes. Find its speed in km/h.
Step-by-step:
Step-by-step:
- Convert time to hours: 30 minutes = 30 ÷ 60 = 0.5 hours
- Use the formula: Speed = Distance ÷ Time
- Distance = 33 km, Time = 0.5 hours
- Speed = 33 km ÷ 0.5 hours = 33 × 2 = 66 km/h
- So, the car's speed is 66 km/h.
Conversion of Units of Speed
Speed units can be converted to match the required format.
To convert km/h to m/s: Multiply by 5/18.
- Reason: 1 km = 1,000 m, 1 hour = 3,600 s, so 1 km/h = 1,000 m ÷ 3,600 s = 5/18 m/s
To convert km/h to cm/s: Multiply by 250/9.
- Reason: 1 km = 100,000 cm, 1 hour = 3,600 s, so 1 km/h = 100,000 cm ÷ 3,600 s = 250/9 cm/s
To convert m/s to km/h: Multiply by 18/5.
- Reason: 1 m/s = (1 m ÷ 1,000) km ÷ (1 s ÷ 3,600) h = 3,600 ÷ 1,000 = 18/5 km/h
To convert cm/s to km/h: Multiply by 9/250.
- Reason: 1 cm/s = (1 cm ÷ 100,000) km ÷ (1 s ÷ 3,600) h = 3,600 ÷ 100,000 = 9/250 km/h
Example: Convert 90 km/h to m/s.
Step-by-step:
Step-by-step:
- Use the conversion factor: Multiply by 5/18
- Speed = 90 × 5/18 = (90 × 5) ÷ 18 = 450 ÷ 18 = 25 m/s
- So, 90 km/h = 25 m/s.
Solved Examples
Example 1: A train travels at 125 km/h for 3 hours. Find the distance covered.
Step-by-step:
Step-by-step:
- Use the formula: Distance = Speed × Time
- Speed = 125 km/h, Time = 3 hours
- Distance = 125 × 3 = 375 km
- So, the train covers 375 km.
Example 2: A motorbike travels 56 km at a speed of 42 km/h. Find the time taken.
Step-by-step:
Step-by-step:
- Use the formula: Time = Distance ÷ Speed
- Distance = 56 km, Speed = 42 km/h
- Time = 56 ÷ 42 = 4/3 hours = 1 hour 20 minutes
- So, the time taken is 1 hour 20 minutes.
Example 3: Anant runs 250 meters in 50 seconds. Find:
(a) his speed
(b) distance covered in 10 seconds
(c) time taken to cover 1/2 km
Step-by-step:
(a) Speed = Distance ÷ Time = 250 m ÷ 50 s = 5 m/s
(b) Distance = Speed × Time = 5 m/s × 10 s = 50 m
(c) Distance = 1/2 km = 500 m, Time = Distance ÷ Speed = 500 m ÷ 5 m/s = 100 s
So, speed = 5 m/s, distance = 50 m, time = 100 s.
(a) his speed
(b) distance covered in 10 seconds
(c) time taken to cover 1/2 km
Step-by-step:
(a) Speed = Distance ÷ Time = 250 m ÷ 50 s = 5 m/s
(b) Distance = Speed × Time = 5 m/s × 10 s = 50 m
(c) Distance = 1/2 km = 500 m, Time = Distance ÷ Speed = 500 m ÷ 5 m/s = 100 s
So, speed = 5 m/s, distance = 50 m, time = 100 s.
Example 4: A motorist travels 50 km at 40 km/h and 70 km at 60 km/h. Find:
(a) total time taken
(b) average speed
Step-by-step:
(a) total time taken
(b) average speed
Step-by-step:
(a) Time for 50 km = 50 ÷ 40 = 5/4 hours
- Time for 70 km = 70 ÷ 60 = 7/6 hours
- Total time = 5/4 + 7/6 = (15 + 14)/12 = 29/12 hours
(b) Average speed = Total distance ÷ Total time = (50 + 70) ÷ (29/12) = 120 × 12/29 = 49 19/29 km/h
- So, total time = 29/12 hours, average speed = 49 19/29 km/h.
Example 5: Two athletes X and Y run from the same point at 10 km/h and 12 km/h for 3 hours. Find the distance between them if they run:
(a) in the same direction
(b) in opposite directions
Step-by-step:
(a) in the same direction
(b) in opposite directions
Step-by-step:
(a) Distance by X = 10 × 3 = 30 km, Distance by Y = 12 × 3 = 36 km
- Distance between them (same direction) = 36 - 30 = 6 km
(b) Distance between them (opposite directions) = 30 + 36 = 66 km
- So, same direction = 6 km, opposite directions = 66 km.
Example 6: An aeroplane covers 1,500 km in 2.5 hours. Find its speed in:
(a) m/s
(b) km/min
Step-by-step:
(a) m/s
(b) km/min
Step-by-step:
(a) Speed = 1,500 km ÷ 2.5 h = 600 km/h
- Convert to m/s: 600 × 5/18 = 166 2/3 m/s
(b) Speed = 600 km/h ÷ 60 min = 10 km/min
- So, speed = 166 2/3 m/s, 10 km/min.
Example 7: A 200 m long train travels at 90 km/h. Find the time to pass:
(a) a pole
(b) a 325 m long platform
Step-by-step:
(a) a pole
(b) a 325 m long platform
Step-by-step:
Convert speed: 90 km/h = 90 × 5/18 = 25 m/s
(a) Distance = 200 m, Time = 200 ÷ 25 = 8 s
(b) Distance = 200 + 325 = 525 m, Time = 525 ÷ 25 = 21 s
So, the time to pass the pole = 8 s, platform = 21 s.
The document Speed, Distance, and Time Chapter Notes | Mathematics Class 6 ICSE is a part of the Class 6 Course Mathematics Class 6 ICSE.
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FAQs on Speed, Distance, and Time Chapter Notes - Mathematics Class 6 ICSE
| 1. What is speed and how is it defined in physics? |  |
Ans. Speed is defined as the distance traveled by an object in a given amount of time. In physics, speed is typically measured in units such as meters per second (m/s) or kilometers per hour (km/h). It represents how fast an object is moving regardless of its direction.
| 2. What are the common units of speed used in different contexts? | |
Ans. Common units of speed include meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph). Meters per second is often used in scientific contexts, while kilometers per hour and miles per hour are frequently used in everyday scenarios, such as driving.
| 3. How can we convert speed from one unit to another? | |
Ans. To convert speed from one unit to another, you can use conversion factors. For example, to convert from kilometers per hour (km/h) to meters per second (m/s), you can multiply by 5/18. Conversely, to convert from meters per second to kilometers per hour, you multiply by 18/5. This allows for easy interchangeability between units.
| 4. Can you provide a simple example of calculating speed using distance and time? | |
Ans. Certainly! If a car travels a distance of 150 kilometers in 3 hours, the speed can be calculated using the formula: Speed = Distance ÷ Time. Thus, Speed = 150 km ÷ 3 h = 50 km/h. Therefore, the car's speed is 50 kilometers per hour.
| 5. What is the relationship between speed, distance, and time in a formula? | |
Ans. The relationship between speed, distance, and time is described by the formula: Speed = Distance ÷ Time. This means that if you know any two of these variables, you can easily calculate the third. For example, if you have the speed and time, you can find the distance by rearranging the formula to Distance = Speed × Time.
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