Constant speed is a fundamental concept in physics that describes the motion of an object where the rate of change in position remains the same over a given period of time. This means that the distance covered by the object is directly proportional to the time taken. In this comprehensive guide, we will explore various examples of constant speed, delving into the technical details, formulas, and numerical problems to provide a thorough understanding for physics students.
Understanding Constant Speed
Constant speed, also known as uniform speed or constant velocity, is a state of motion where an object’s speed remains the same throughout its journey. This can be expressed mathematically using the formula:
{eq}speed = \frac{distance}{time} {/eq}
where speed is measured in units of distance per unit of time, such as miles per hour (mph), kilometers per hour (km/h), or meters per second (m/s). The distance covered by the object is directly proportional to the time taken, and this relationship remains constant throughout the motion.
Examples of Constant Speed
1. Car Traveling at a Constant Speed
Consider a car traveling at a constant speed of 60 miles per hour (mph). This means that the car covers a distance of 60 miles for every hour it travels. For instance, if the car travels for 2 hours, it will cover a distance of 120 miles (60 mph × 2 hours).
The mathematical expression for this scenario is:
{eq}speed = \frac{distance}{time} \implies 60 \text{ mph} = \frac{distance}{time} \implies distance = 60 \times time {/eq}
where the distance is directly proportional to the time taken.
Example Problem: A car is traveling at a constant speed of 70 mph. Calculate the distance covered by the car in 3 hours.
Given:
– Speed of the car = 70 mph
– Time = 3 hours
Using the formula:
{eq}distance = speed \times time {/eq}
Substituting the values:
{eq}distance = 70 \text{ mph} \times 3 \text{ hours} = 210 \text{ miles} {/eq}
Therefore, the car will cover a distance of 210 miles in 3 hours.
2. Person Walking at a Constant Speed
Consider a person walking at a constant speed of 3 miles per hour (mph). If the person walks for 1.5 hours, they will cover a distance of 4.5 miles (3 mph × 1.5 hours).
The mathematical expression for this scenario is:
{eq}speed = \frac{distance}{time} \implies 3 \text{ mph} = \frac{distance}{time} \implies distance = 3 \times time {/eq}
where the distance is directly proportional to the time taken.
Example Problem: A person is walking at a constant speed of 4 km/h. Calculate the distance covered by the person in 2.5 hours.
Given:
– Speed of the person = 4 km/h
– Time = 2.5 hours
Using the formula:
{eq}distance = speed \times time {/eq}
Substituting the values:
{eq}distance = 4 \text{ km/h} \times 2.5 \text{ hours} = 10 \text{ km} {/eq}
Therefore, the person will cover a distance of 10 km in 2.5 hours.
3. Cyclist Maintaining a Constant Speed
Consider a cyclist maintaining a constant speed of 15 miles per hour (mph). If the cyclist rides for 3 hours, they will cover a distance of 45 miles (15 mph × 3 hours).
The mathematical expression for this scenario is:
{eq}speed = \frac{distance}{time} \implies 15 \text{ mph} = \frac{distance}{time} \implies distance = 15 \times time {/eq}
where the distance is directly proportional to the time taken.
Example Problem: A cyclist is traveling at a constant speed of 20 km/h. Calculate the distance covered by the cyclist in 4.5 hours.
Given:
– Speed of the cyclist = 20 km/h
– Time = 4.5 hours
Using the formula:
{eq}distance = speed \times time {/eq}
Substituting the values:
{eq}distance = 20 \text{ km/h} \times 4.5 \text{ hours} = 90 \text{ km} {/eq}
Therefore, the cyclist will cover a distance of 90 km in 4.5 hours.
4. Train Traveling at a Constant Speed
Consider a train traveling at a constant speed of 100 kilometers per hour (km/h). If the train travels for 5 hours, it will cover a distance of 500 kilometers (100 km/h × 5 hours).
The mathematical expression for this scenario is:
{eq}speed = \frac{distance}{time} \implies 100 \text{ km/h} = \frac{distance}{time} \implies distance = 100 \times time {/eq}
where the distance is directly proportional to the time taken.
Example Problem: A train is traveling at a constant speed of 150 km/h. Calculate the distance covered by the train in 3.2 hours.
Given:
– Speed of the train = 150 km/h
– Time = 3.2 hours
Using the formula:
{eq}distance = speed \times time {/eq}
Substituting the values:
{eq}distance = 150 \text{ km/h} \times 3.2 \text{ hours} = 480 \text{ km} {/eq}
Therefore, the train will cover a distance of 480 km in 3.2 hours.
5. Runner Maintaining a Constant Pace
Consider a runner maintaining a constant pace of 8 kilometers per hour (km/h). If the runner runs for 45 minutes, they will cover a distance of 6 kilometers (8 km/h × 0.75 hours, where 45 minutes is equal to 0.75 hours).
The mathematical expression for this scenario is:
{eq}speed = \frac{distance}{time} \implies 8 \text{ km/h} = \frac{distance}{time} \implies distance = 8 \times time {/eq}
where the distance is directly proportional to the time taken.
Example Problem: A runner is maintaining a constant pace of 12 km/h. Calculate the distance covered by the runner in 1.5 hours.
Given:
– Speed of the runner = 12 km/h
– Time = 1.5 hours
Using the formula:
{eq}distance = speed \times time {/eq}
Substituting the values:
{eq}distance = 12 \text{ km/h} \times 1.5 \text{ hours} = 18 \text{ km} {/eq}
Therefore, the runner will cover a distance of 18 km in 1.5 hours.
Additional Constant Speed Examples
- Airplane Traveling at a Constant Speed: An airplane traveling at a constant speed of 500 mph covers a distance of 2,500 miles in 5 hours.
- Boat Sailing at a Constant Speed: A boat sailing at a constant speed of 20 knots (1 knot = 1.852 km/h) covers a distance of 100 nautical miles in 5 hours.
- Elevator Moving at a Constant Speed: An elevator moving at a constant speed of 1.5 m/s covers a distance of 15 meters in 10 seconds.
- Conveyor Belt Moving at a Constant Speed: A conveyor belt moving at a constant speed of 0.5 m/s carries an object a distance of 10 meters in 20 seconds.
- Satellite Orbiting at a Constant Speed: A satellite orbiting the Earth at a constant speed of 28,000 km/h completes one full revolution around the Earth in 90 minutes.
These additional examples further illustrate the concept of constant speed and its applications in various real-world scenarios.
Conclusion
In this comprehensive guide, we have explored various examples of constant speed, delving into the technical details, formulas, and numerical problems to provide a thorough understanding for physics students. By understanding the concept of constant speed and its mathematical representation, students can effectively apply this knowledge to solve a wide range of problems in physics and everyday life.
References
- https://study.com/skill/learn/how-to-find-a-constant-speed-explanation.html
- https://kellyoshea.blog/2012/11/19/building-the-constant-velocity-model/
- https://www.fullstory.com/quantitative-data/
- https://www.honolulu.hawaii.edu/instruct/natsci/science/brill/sci122/SciLab/L4/DescMotLab.html
- https://openoregon.pressbooks.pub/bodyphysics/chapter/human-walking-speed-remote-learning-compatible/
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