Speed refers to how fast an object is moving over a certain distance. Speed is typically measured in units of distance per unit time, such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph). Speed is a scalar quantity, meaning it only has magnitude (a numerical value) and no direction.
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The average speed of an object is the total distance traveled divided by the total time taken. The formula is:
Average Speed = Total Distance / Total Time
Or:
s = d/t
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Example speed calculations:
1. A car travels 150 miles in 3 hours
Average speed = 150 miles ÷ 3 hours = 50 mph
2. A runner completes a 5-kilometer race in 25 minutes
Average speed = 5 km ÷ 25 min = 0.2 km/min (or 12 km/h)
3. A plane flies 2,400 miles in 4 hours
Average speed = 2,400 miles ÷ 4 hours = 600 mph
4. A cyclist travels 30 km in 1.5 hours.
Average Speed = 30 km / 1.5 hours = 20 km/h
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The distance formula is derived from the speed formula.
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The formula is:
Distance = Speed × Time
or
d = s × t
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Examples:
1: A train travels at a speed of 60 km/h for 3 hours. How far does it go?
Distance = 60 km/h × 4 hours = 240 km
2: A flight-jet flies at a speed of 900 km/h for 2.5 hours. What is the distance covered?
Distance = 900 km/h × 2.5 hours = 2250 km
3: A person walks at a speed of 4 m/s for 120 seconds. How far do they walk?
Distance = 4 m/s × 120 s = 480 m
4: A car travels at an average speed of 60 mph for 3 hours. What is the distance it covered:
Distance = 60 mph × 3 hours = 180 miles
5: A runner runs at a speed of 8 km/h for 2.5 hours. What distance did it run?
Distance = 8 km/h × 2.5 hours = 20 km
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The time duration formula is also derived from the speed formula. It calculates the time taken to travel a certain distance at a given speed. The formula is:
Time = Distance / Speed
or
t = d / s
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Here are 3 examples:
1: A car travels 200 km at a speed of 50 km/h. How long does it take?
Time = 200 km / 50 km/h = 4 hours
2: A plane covers 1800 km at a speed of 600 km/h. How long does the journey take?
Time = 1800 km / 600 km/h = 3 hours
3: A cyclist travels 15 km at a speed of 10 km/h. How long does it take?
Time = 15 km / 10 km/h = 1.5 hours
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To calculate the average speed of a car, use this formula
Average Speed = Total Distance / Total Time.
A car travels 240 km in 4 hours. What is its average speed?
If the car travels at varying speeds during the journey, you still use the total distance and total time to find the average speed, regardless of the changes in speed.
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For example: If a car travels from City A to City B (120 miles) in 2 hours, then returns (another 120 miles) in 3 hours:
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Average speed and average velocity are related but distinct concepts, let’s see the differences:
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Aspect | Average Speed | Average Velocity |
Definition | Total distance traveled divided by total time. | Total displacement divided by total time. |
Type | Scalar (only magnitude). | Vector (magnitude and direction). |
Formula | s = Total Distance / Total Time | v = Total Displacement / Total Time |
Direction | Does not consider direction. | Considers direction of motion. |
Example | A car travels 100 km east, then 100 km west in 4 hours. Average speed = 200 km / 4 hours = 50 km/h. | Same car: Displacement = 0 km (back to start), so average velocity = 0 km/h. |
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The most economical driving speed varies depending on the vehicle, road conditions, and other factors. However, according to the United States Department of Energy, the most fuel-efficient speed for most vehicles is between 40 and 60 mph (64 and 97 km/h). Driving at this speed can help you save fuel and reduce your carbon footprint.
Here are some general guidelines for the most economical driving speeds:
Tip: To maximize fuel efficiency, drive at a steady speed, avoid rapid acceleration or braking, and use cruise control on highways when appropriate.
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