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
In a circular race of 2500 m, a man and a woman start from a point towards opposite directions with speeds of 37 km/h and 35 km/h, respectively. After how much time from the start of the race will they meet for the first time?
- X and Yrun a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
A train of length 600 meters passes another train of length 1000 meters moving in the opposite direction in 96 seconds. If the speed of both the trains is the same, then what is the speed of each train?
The distance between Delhi and Patna is $480$ km. A train starts from Delhi and travels towards Patna at a speed of $60$ kmph. Another train starts from Patna towards Delhi at a speed of $80$ kmph, but starts $1$ hour after the first train. In how much time, after the first train started, will they meet each other?
Ram traveling at the speed of 3 km/h reaches 15 minutes late. Had he walked at 4 km/h, he would have reached 15 minutes earlier. How much distance does Ram have to cover?
