A person can walk at a speed of 0.5 meters/second. How far will he walk in 8 minutes?
240 m
Calculating Walking Distance Based on Speed and Time
This problem asks us to determine the distance a person walks given their speed and the duration of their walk. We are provided with the speed in meters per second and the time in minutes. To solve this, we need to ensure all units are consistent before applying the formula relating distance, speed, and time.
Understanding the Given Information
- Speed of the person: 0.5 meters per second
- Time spent walking: 8 minutes
Unit Conversion: Minutes to Seconds
The speed is given in meters per second, but the time is given in minutes. To use the formula \( \text{Distance} = \text{Speed} \times \text{Time} \), the units of time must be the same. We need to convert minutes into seconds.
There are 60 seconds in 1 minute.
So, to convert 8 minutes to seconds, we multiply 8 by 60:
\( \text{Time in seconds} = \text{Time in minutes} \times 60 \)
\( \text{Time in seconds} = 8 \times 60 \)
\( \text{Time in seconds} = 480 \text{ seconds} \)
Calculating the Distance Walked
Now that we have the speed in meters per second and the time in seconds, we can calculate the distance walked using the formula:
\( \text{Distance} = \text{Speed} \times \text{Time} \)
Substitute the given speed (0.5 m/s) and the converted time (480 s) into the formula:
\( \text{Distance} = 0.5 \, \text{m/s} \times 480 \, \text{s} \)
\( \text{Distance} = \frac{1}{2} \times 480 \, \text{m} \)
\( \text{Distance} = 240 \, \text{m} \)
The person will walk 240 meters in 8 minutes.
Comparing with Options
Let's look at the given options:
- Option 1: 250 m
- Option 2: 200 m
- Option 3: 120 m
- Option 4: 240 m
Our calculated distance is 240 m, which matches Option 4.
| Given | Value | Units |
|---|---|---|
| Speed | 0.5 | meters/second (m/s) |
| Time | 8 | minutes (min) |
| Conversion | Calculation | Result |
|---|---|---|
| Time (minutes to seconds) | \( 8 \text{ min} \times 60 \text{ s/min} \) | 480 seconds |
| Calculation | Formula | Result |
|---|---|---|
| Distance | \( \text{Distance} = \text{Speed} \times \text{Time} \) | \( 0.5 \, \text{m/s} \times 480 \, \text{s} = 240 \, \text{m} \) |
Revision Table: Speed, Distance, Time Calculation
Here's a quick summary of the concepts used:
| Concept | Definition/Formula |
|---|---|
| Speed | Rate at which distance is covered per unit of time. \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \) |
| Distance | Total length covered during motion. \( \text{Distance} = \text{Speed} \times \text{Time} \) |
| Time | Duration of the motion. \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \) |
| Unit Consistency | All quantities must be in compatible units (e.g., meters and seconds, or kilometers and hours) before calculation. |
Additional Information: Understanding Units
It is crucial in physics and mathematics problems to pay close attention to units. When performing calculations, units must be consistent. If they are not, you must convert them. Common units for speed, distance, and time include:
- Speed: meters per second (m/s), kilometers per hour (km/h), miles per hour (mph)
- Distance: meters (m), kilometers (km), miles, feet
- Time: seconds (s), minutes (min), hours (h)
Incorrect unit usage is a common source of errors in problems involving speed, distance, and time calculations.
Important Questions from Relative Speed
Two trains start from places A and B. respectively, and travel towards each other at the speeds of 60 km/h and 50 km/h. respectively. By the time they meet, the faster train has travelled 110 km more than the slower train. What is the distance between A and B?
A train can cross a tunnel of length 600 m in 54 seconds, and it can cross a 350 m long bridge in 36 seconds. Which of the following statements is/are correct?
(i) The speed of the train is 60 km/h.
(ii) The length of the train is 150 m
Raghu and Raman start together to walk a certain equal distance at a speed of 10 km/h and 8 km/h, respectively. Raghu arrives 30 minutes before Raman arrives. Find the distance between the start and the end point.
A and B started simultaneously and proceeded towards each other from places X and Y, respectively. After meeting each other at a certain point on the way, A and B took 3.2 hours and 1.8 hours, to reach Y and X, respectively. If the speed of B was 12 km/h, then the speed (in km/h) of A was:
Anil started his journey in the morning. Till 10 a.m., he covered \(\frac{1}{2}\) of his journey, and on the same day till 1 a.m., he covered \(\frac{4}{5}\) of his journey. At what time did he start his journey?
