A person crosses a 1600 m long street in 4 min. What is his speed (in km/h)?
24
Calculating Speed in km/h
The problem asks us to find the speed of a person who crosses a street. We are given the distance and the time taken, but the units are in meters and minutes, and we need to express the speed in kilometers per hour (km/h).
Understanding the Given Information
- Distance covered: 1600 meters
- Time taken: 4 minutes
Unit Conversion for Speed Calculation
To find the speed in km/h, we first need to convert the given distance from meters to kilometers and the time from minutes to hours.
Converting Distance from Meters to Kilometers
There are 1000 meters in 1 kilometer. So, to convert meters to kilometers, we divide the distance in meters by 1000.
Distance in km = Distance in meters / 1000
Distance = \( \frac{1600 \text{ m}}{1000 \text{ m/km}} = 1.6 \text{ km} \)
Converting Time from Minutes to Hours
There are 60 minutes in 1 hour. So, to convert minutes to hours, we divide the time in minutes by 60.
Time in hours = Time in minutes / 60
Time = \( \frac{4 \text{ min}}{60 \text{ min/h}} = \frac{4}{60} \text{ h} = \frac{1}{15} \text{ h} \)
Applying the Speed Formula
The formula for speed is:
Speed = \( \frac{\text{Distance}}{\text{Time}} \)
Now, we can substitute the converted distance and time values into the formula:
Speed = \( \frac{1.6 \text{ km}}{\frac{1}{15} \text{ h}} \)
To divide by a fraction, we multiply by its reciprocal:
Speed = \( 1.6 \times 15 \text{ km/h} \)
Let's perform the multiplication:
\( 1.6 \times 15 = \frac{16}{10} \times 15 = \frac{8}{5} \times 15 = 8 \times 3 = 24 \)
So, the speed is 24 km/h.
Final Answer
The person's speed is 24 km/h.
Revision Table: Units and Conversions
| Quantity | Common Unit | Conversion to SI/Standard Unit |
|---|---|---|
| Distance | meter (m) | Already SI unit |
| Distance | kilometer (km) | 1 km = 1000 m |
| Time | second (s) | Already SI unit |
| Time | minute (min) | 1 min = 60 s |
| Time | hour (h) | 1 h = 60 min = 3600 s |
| Speed | meter per second (m/s) | SI unit |
| Speed | kilometer per hour (km/h) | 1 km/h = \( \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \) m/s |
Additional Information: Understanding Speed
Speed is a scalar quantity that measures how fast an object is moving. It is defined as the distance traveled per unit of time. The standard International System of Units (SI) unit for speed is meters per second (m/s), but kilometers per hour (km/h) is commonly used, especially for vehicle speeds.
Key concepts related to speed:
- Constant Speed: When an object covers equal distances in equal intervals of time, its speed is constant.
- Variable Speed: When an object covers unequal distances in equal intervals of time, its speed is variable.
- Average Speed: For an object moving with variable speed, the average speed is the total distance traveled divided by the total time taken.
- Instantaneous Speed: The speed of an object at a particular moment in time.
Understanding unit conversions is crucial for solving physics problems involving distance, time, and speed. Common conversions include m <-> km, s <-> min <-> h, and m/s <-> km/h.
Important Questions from Speed Time and Distance
The average speed of a train is 180% of the average speed of a car. The car covers a distance of 990 km in 15 hours. The time taken (in hours) by the train to cover the distance of 891 km is:
If Rohit can cover a distance of 1188 km in 22 hours, then what is the speed of Rohit?
A train is moving at 72 km/hrs. The distance covers in 15 minutes by the train is:
If Sonu is driving a car at a speed of 20 m/s, then in how much time Sonu will cover a distance of 936 km?
A 725 m long train passes a tunnel 235 m long in 48 seconds. Find the speed of the train.
