Speed, Time and Distance Lesson: Formulas, Conversion & Examples
Lesson Overview
- What Are Speed, Time, and Distance?
- Relationship Between Speed, Time, and Distance
- Formula for Speed, Time, and Distance
- Conversion of Speed, Time and Distance
- Examples of Speed, Time and Distance
Everything moves. A speeding car, a falling leaf, even the Earth rotating on its axis. To understand this movement, we need to grasp the relationship between speed, time, and distance.
Speed measures how fast something moves. Time tracks how long the movement lasts. Distance tells us how far something travels. These three concepts are linked – change one, and the others change too.
What Are Speed, Time, and Distance?
Speed is the rate at which an object changes its position. It is a scalar quantity, meaning it only has magnitude (how fast) and not direction.
- Example: A car traveling at 60 kilometers per hour. This tells us how fast the car is moving, but not in which direction.
Time is the measure of the duration between two events. It is a fundamental physical quantity and is often considered a scalar quantity.
- Example: A train journey that takes 3 hours. This tells us the duration of the journey.
Distance is the total length of the path traveled by an object. It is a scalar quantity, measuring the overall ground covered, regardless of the direction of motion.
Example: The distance between California and Texas is approximately 1400 kilometers.
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Relationship Between Speed, Time, and Distance
Speed, time, and distance are not isolated concepts; they exist in a dynamic relationship where a change in one inevitably influences the others.
Key Principles:
- Direct Proportionality of Speed and Distance: When time is constant, speed and distance are directly proportional. Greater speed leads to greater distance covered, and vice versa.
- Inverse Proportionality of Speed and Time: When distance is constant, speed and time are inversely proportional. Higher speed results in shorter time taken, and vice versa.
- Combined Effect: When both speed and time change, their combined effect determines the distance. Increasing speed while decreasing time can lead to varying distances depending on the magnitude of change in each factor.
Constant Speed: When speed remains constant, distance and time are directly proportional. Longer time leads to greater distance, and vice versa.
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Formula for Speed, Time, and Distance
There are some formulas that help calculate the relationship between speed, time, and distance.
| Term | Formula | Description | Units |
| Speed | Speed = Distance / Time | The rate at which an object moves. | m/s, km/h, mph |
| Time | Time = Distance / Speed | The duration of an event or journey. | s, min, h |
| Distance | Distance = Speed x Time | The length of the path travelled by an object. | m, km, mi |
| Average Speed | Average Speed = Total Distance / Total Time | The average rate of motion over a given time interval. | m/s, km/h, mph |
| Average Speed (when distance travelled is constant) | Average Speed = 2 * Speed 1 * Speed 2 / (Speed 1 + Speed 2) | Used when an object travels the same distance at two different speeds. | m/s, km/h, mph |
| Relative speed (moving in the opposite direction) | Relative Speed = Speed 1 + Speed 2 | The combined speed of two objects moving towards each other. | m/s, km/h, mph |
| Relative speed (moving in the same direction) | Relative Speed = Speed 1 - Speed 2 | The difference in speed between two objects moving in the same direction. | m/s, km/h, mph |
Conversion of Speed, Time and Distance
When dealing with speed, time, and distance problems, it's crucial to ensure that your units are consistent. This often involves converting between different units of measurement.
- Converting Speed
To convert kilometers per hour (km/h) to meters per second (m/s): Multiply the speed in km/h by 5/18.
Example:
Convert 72 km/h to m/s.
= 72 km/h * (5/18) = 20 m/s
To convert meters per second (m/s) to kilometers per hour (km/h): Multiply the speed in m/s by 18/5.
Example:
Convert 15 m/s to km/h.
15 m/s * (18/5) = 54 km/h
- Converting Time
To convert hours to minutes: Multiply by 60.
Example:
A movie lasts for 2.5 hours. To find the duration in minutes: 2.5 hours * 60 minutes/hour = 150 minutes
To convert minutes to seconds: Multiply by 60.
Example:
A commercial break is 5 minutes long. To find the duration in seconds: 5 minutes * 60 seconds/minute = 300 seconds
To convert hours to seconds: Multiply by 3600 (60 x 60).
Example:
A flight takes 3 hours. To find the duration in seconds: 3 hours * 3600 seconds/hour = 10,800 seconds
- Converting Distance
To convert kilometers to meters: Multiply by 1000.
Example:
A marathon is approximately 42 kilometers long. To find the equivalent distance in meters: 42 km * 1000 m/km = 42,000 m
To convert meters to centimeters: Multiply by 100.
Example:
A table is 2.5 meters long. To find the length in centimeters: 2.5 m * 100 cm/m = 250 cm
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Examples of Speed, Time and Distance
Example 1. A train travels 450 kilometers in 5 hours. What is its speed?
- Identify the knowns: Distance (D) = 450 km, Time (T) = 5 hours
- Use the formula: Speed (S) = Distance (D) / Time (T)
- Substitute the values: S = 450 km / 5 h
- Calculate: S = 90 km/h
Example 2. A cyclist travels at a speed of 15 km/h and covers a distance of 30 km. How long does it take?
- Identify the knowns: Speed (S) = 15 km/h, Distance (D) = 30 km
- Use the formula: Time (T) = Distance (D) / Speed (S)
- Substitute the values: T = 30 km / 15 km/h
- Calculate: T = 2 hours
Example 3. A plane flies at a speed of 600 km/h for 4 hours. What distance does it cover?
- Identify the knowns: Speed (S) = 600 km/h, Time (T) = 4 hours
- Use the formula: Distance (D) = Speed (S) x Time (T)
- Substitute the values: D = 600 km/h x 4 h
- Calculate: D = 2400 km
Example 4. A car travels 100 km at 40 km/h and then 150 km at 60 km/h. What is the average speed of the car for the entire journey?
- Calculate the time taken for each leg:
- Time for the first 100 km: T1 = 100 km / 40 km/h = 2.5 hours
- Time for the next 150 km: T2 = 150 km / 60 km/h = 2.5 hours
- Calculate the total distance and total time:
- Total distance: 100 km + 150 km = 250 km
- Total time: 2.5 hours + 2.5 hours = 5 hours
- Use the formula: Average Speed = Total Distance / Total Time
- Substitute the values: Average Speed = 250 km / 5 hours
- Calculate: Average Speed = 50 km/h
Example 5. A person travels from point A to point B at a speed of 40 km/h and returns from point B to point A at a speed of 60 km/h. What is the average speed for the entire journey?
- Since the distance is the same for both legs, we can use the simplified formula: Average Speed = (2 * S1 * S2) / (S1 + S2) where S1 and S2 are the speeds for the two legs.
- Substitute the values: Average Speed = (2 * 40 km/h * 60 km/h) / (40 km/h + 60 km/h)
- Calculate: Average Speed = 48 km/h
Example 6. Two cars are moving towards each other, one at a speed of 70 km/h and the other at a speed of 80 km/h. What is their relative speed?
- Use the formula: Relative Speed = Speed of first object + Speed of second object
- Substitute the values: Relative Speed = 70 km/h + 80 km/h
- Calculate: Relative Speed = 150 km/h
Example 7. Two cyclists are moving in the same direction, one at a speed of 20 km/h and the other at a speed of 15 km/h. What is their relative speed?
- Use the formula: Relative Speed = |Speed of faster object - Speed of slower object|
- Substitute the values: Relative Speed = |20 km/h - 15 km/h|
- Calculate: Relative Speed = 5 km/h
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