Speed is one of the most fundamental concepts in physics and everyday life. Whether you're planning a road trip, training for a marathon, or solving physics problems, understanding how to calculate speed is essential. In this comprehensive guide, we'll cover everything you need to know about the speed formula and its applications.
The Speed Formula
The basic formula for calculating speed is remarkably simple:
Where:
- v = speed (velocity)
- d = distance traveled
- t = time taken
Rearranging the Formula
The speed formula can be rearranged to solve for any of the three variables:
Example 1: Calculating Speed
Problem:
A car travels 150 kilometers in 2 hours. What is its average speed?
Solution:
Using the formula: v = d / t
v = 150 km / 2 h
v = 75 km/h
Answer: The car's average speed is 75 km/h.
Example 2: Calculating Distance
Problem:
A cyclist rides at 20 km/h for 3 hours. How far do they travel?
Solution:
Using the formula: d = v × t
d = 20 km/h × 3 h
d = 60 km
Answer: The cyclist travels 60 kilometers.
Example 3: Calculating Time
Problem:
A plane needs to travel 900 km at a speed of 600 km/h. How long will the flight take?
Solution:
Using the formula: t = d / v
t = 900 km / 600 km/h
t = 1.5 hours
Answer: The flight will take 1.5 hours (1 hour 30 minutes).
Units Matter!
When calculating speed, it's crucial that your units are consistent. Common speed units include:
- km/h (kilometers per hour) - used in most countries
- mph (miles per hour) - used in US, UK
- m/s (meters per second) - used in physics
- ft/s (feet per second) - used in engineering
If your distance is in kilometers and time is in hours, your speed will be in km/h. If distance is in meters and time is in seconds, speed will be in m/s.
Common Unit Conversions
| From | To | Multiply by |
|---|---|---|
| km/h | mph | 0.621 |
| mph | km/h | 1.609 |
| m/s | km/h | 3.6 |
| km/h | m/s | 0.278 |
Average Speed vs. Instantaneous Speed
It's important to understand the difference:
Average Speed
Total distance divided by total time. Accounts for all stops, slowdowns, and speed changes during a journey.
Instantaneous Speed
Speed at a specific moment in time. What your car's speedometer shows at any given instant.
Practice Problems
Test your understanding with these problems:
- A train travels 480 km in 4 hours. What is its average speed?
- A runner maintains a speed of 12 km/h for 45 minutes. How far do they run?
- How long will it take to drive 350 miles at 70 mph?
- A swimmer covers 100 meters in 50 seconds. What is their speed in m/s?
Answers
- 120 km/h
- 9 km (12 × 0.75 hours)
- 5 hours
- 2 m/s
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