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
- Ankur jogs on a circular track X at $1 \frac{2}{3}$ m/s and Mahima jogs on track Y at $2 \frac{1}{12}$ m/s. The total length of Tracks X and Y is 0.325 km. Ankur makes 9 rounds of track X in the same time Mahima makes 5 rounds of track Y. The time taken (in seconds) by Mahima to complete one round of track X is:
- Two places, A and B are 3710 kms from each other. A train leaves from A to B at the same time another train leaves B to A. The two trains meet at the end of 35 hours. If the train travelling from A to B travels 35 kmph faster than the other. Find the speed of the faster train. (In kmph)
- A truck, 1575 metres long is running at a speed of 109 km/hr. How many seconds will it take to cross a 1475 metres long train running in the same direction at a speed of 79 km/hr?
- A truck, 1600 metres long is running at a speed of 112 km/hr. How many seconds will it take to cross a 1500 metres long train running in the same direction at a speed of 82 km/hr?
- Two friends 10 km apart start running towards each other at speeds of 10 km/hr and 14 km/hr respectively. After how much time will they meet each other?
