An object travels 20 m in 5 seconds and then another 25 m in 10 seconds. What is the average speed?
3 m/sec
Calculating Average Speed: A Step-by-Step Physics Solution
This problem asks us to determine the average speed of an object that moves in two distinct segments. Average speed is a fundamental concept in physics that describes the overall rate at which an object covers distance over a period of time.
Understanding Average Speed
Average speed is defined as the total distance traveled divided by the total time taken for the entire journey. It doesn't consider the variations in speed during different parts of the journey, only the overall outcome.
The formula for average speed is:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Calculating Total Distance Traveled
The object travels in two parts:
- First part: 20 meters
- Second part: 25 meters
To find the total distance, we add the distances of these two segments:
\(\text{Total Distance} = \text{Distance}_1 + \text{Distance}_2\)
\(\text{Total Distance} = 20 \text{ m} + 25 \text{ m}\)
\(\text{Total Distance} = 45 \text{ m}\)
Calculating Total Time Taken
Similarly, the time taken for the two parts of the journey are:
- First part: 5 seconds
- Second part: 10 seconds
To find the total time, we add the times for these two segments:
\(\text{Total Time} = \text{Time}_1 + \text{Time}_2\)
\(\text{Total Time} = 5 \text{ s} + 10 \text{ s}\)
\(\text{Total Time} = 15 \text{ s}\)
Final Calculation of Average Speed
Now that we have the total distance and the total time, we can calculate the average speed using the formula:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Substitute the calculated values:
\(\text{Average Speed} = \frac{45 \text{ m}}{15 \text{ s}}\)
\(\text{Average Speed} = 3 \text{ m/s}\)
Therefore, the average speed of the object is 3 m/sec.
Analysis of Options
Let's compare our calculated average speed with the given options:
- Option 1: 5 m/sec
- Option 2: 3 m/sec
- Option 3: 4 m/sec
- Option 4: 2 m/sec
Our calculated value of 3 m/sec matches Option 2.
Revision Table: Key Concepts
| Concept | Definition | Formula |
|---|---|---|
| Average Speed | Total distance traveled per unit of total time taken. | \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\) |
| Distance | The total length of the path covered by an object. | Sum of individual distances |
| Time | The duration taken for the motion. | Sum of individual times |
Additional Information on Speed and Velocity
While average speed is the total distance divided by total time, average velocity is defined as the total displacement divided by the total time. Displacement is a vector quantity representing the change in position, whereas distance is a scalar quantity representing the total path length.
- Speed: A scalar quantity, only has magnitude (e.g., 3 m/s).
- Velocity: A vector quantity, has both magnitude and direction (e.g., 3 m/s East).
- In straight-line motion without changing direction, the magnitude of average velocity equals average speed.
- When an object changes direction, the total distance is greater than the magnitude of the displacement, and thus average speed is greater than the magnitude of average velocity.
This question focused purely on average speed, requiring only the total distance and total time.
Important Questions from Average Speed
A car covers the first 41 km of its journey in 45 min and covers the remaining 23 km in 35 min. What is the average speed (in m/sec) of the car?
Akhil drives a car from his home to office at an average speed of 50 km/h and reaches office 10 minutes early. But one day due to some problem with the car, he could drive at an average speed of 30 km/h only and reached office 10 minutes late. How far is his office from home ?
During a flight of 900 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 300 km/h and the time of flight increased by 30 min. The original duration of the flight was :
If a man travels from A to B at a speed of 50 km/h and returns by increasing his speed by 40%, then find his average speed (to 2 decimal places) for both the trips.
A man travels a distance of 420 km by train which moves at the speed of 75 km/h and returns back by car at the speed of 50 km/h. Find his average speed for the whole journey.
