Which of the following relations represents the relationship between the average speed, time and distance correctly?

Options

A. `Average speed =distancexxtime`
B. `"Average speed" = ("total distance")/("total time")`
C. Time = average speed + distance
D. Distance = average speed-time

Answer

To solve the question regarding the relationship between average speed, time, and distance, we can follow these steps:

### Step 1: Understand the Definitions
- **Distance (d)**: This is the total path length traveled, regardless of direction. It is a scalar quantity.
- **Time (t)**: This is the duration over which the distance is traveled.
- **Average Speed (v)**: This is defined as the total distance traveled divided by the total time taken.

### Step 2: Write the Formula for Average Speed
The formula for average speed can be expressed mathematically as:
\[ v = \frac{d}{t} \]
Where:
- \( v \) is the average speed,
- \( d \) is the total distance,
- \( t \) is the total time.

### Step 3: Rearranging the Formula
From the formula \( v = \frac{d}{t} \), we can rearrange it to express the relationship between distance, speed, and time:
\[ d = v \cdot t \]
This shows that distance is equal to average speed multiplied by time.

### Step 4: Identify the Correct Relation
From the above derivation, we can conclude that the correct relationship among average speed, time, and distance is:
- Total Distance = Average Speed × Total Time

### Conclusion
The correct relation that represents the relationship between average speed, time, and distance is:
\[ d = v \cdot t \]