Ram records the odometer readings of his car for the distance covered from 2000 km at the start of his journey and 2400 km at the end of the journey after 8 hours. What is the average speed of the car?
50 km/h
Understanding the Average Speed Calculation
The problem asks us to calculate the average speed of a car during a journey. We are given the starting and ending odometer readings, which tell us the total distance covered, and the time taken for the journey.
Calculating the Total Distance Covered
The odometer measures the total distance a vehicle has traveled. To find the distance covered during this specific journey, we subtract the initial odometer reading from the final odometer reading.
Initial odometer reading = 2000 km
Final odometer reading = 2400 km
Total distance covered = Final reading - Initial reading
Total distance covered = \(2400 \text{ km} - 2000 \text{ km}\)
Total distance covered = \(400 \text{ km}\)
Calculating the Average Speed
Average speed is defined as the total distance traveled divided by the total time taken. The formula for average speed is:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
We have calculated the total distance as 400 km, and the time taken is given as 8 hours.
Total Distance = 400 km
Total Time = 8 hours
Now, we can plug these values into the average speed formula:
\[ \text{Average Speed} = \frac{400 \text{ km}}{8 \text{ hours}} \]
\[ \text{Average Speed} = 50 \text{ km/h} \]
Final Answer for Average Speed
The average speed of the car during the journey is 50 km/h.
| Concept | Description | Formula |
|---|---|---|
| Distance Covered | Change in odometer reading | Final Reading - Initial Reading |
| Average Speed | Total distance per unit of total time | Total Distance / Total Time |
Revision Table: Speed and Distance Calculations
| Quantity | Symbol | Unit (SI) | How to find |
|---|---|---|---|
| Distance | \(d\) | meter (m) | Speed \(\times\) Time (if speed is constant) |
| Time | \(t\) | second (s) | Distance / Speed (if speed is constant) |
| Speed | \(v\) | meter/second (m/s) | Distance / Time |
| Average Speed | \(v_{avg}\) | meter/second (m/s) | Total Distance / Total Time |
Additional Information on Speed, Velocity, and Distance
In physics, speed is a scalar quantity that measures how fast an object is moving, defined as the rate of change of distance. Velocity, on the other hand, is a vector quantity that includes both speed and direction. In this problem, since we are asked for average speed and only given distance and time information without direction changes being relevant to the calculation, average speed is the appropriate concept.
Odometer readings directly give us the total distance traveled along the path, regardless of turns or changes in direction. This is different from displacement, which is the straight-line distance between the start and end points.
The units must be consistent when calculating speed. In this case, distance is in kilometers (km) and time is in hours (h), so the average speed is naturally calculated in kilometers per hour (km/h). If the units were different (e.g., meters and seconds), the result would be in meters per second (m/s), which is the standard SI unit for speed.
Understanding the difference between instant speed (speed at a particular moment) and average speed (speed over an entire journey) is crucial. The odometer and timer help us calculate the average speed for the whole trip.
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