A car travels with the speed of 40 km/hr for first hour and 60 km/hr for next hour. What will be the average speed of the car?
50 km/hr
Understanding Average Speed Calculation
The question asks us to find the average speed of a car that travels at different speeds during different time intervals. Average speed is defined as the total distance traveled divided by the total time taken for the journey.
The formula for average speed is:
\text{Average Speed} = \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}}
Step-by-Step Calculation of Car's Average Speed
Let's break down the problem into steps to calculate the total distance and total time.
Step 1: Calculate Distance Traveled in the First Hour
The car travels at a speed of 40 km/hr for the first hour.
- Speed in the first hour = 40 km/hr
- Time in the first hour = 1 hour
Distance traveled in the first hour is calculated using the formula: Distance = Speed $\times$ Time.
\text{Distance}_1 = 40 \text{ km/hr} \times 1 \text{ hr} = 40 \text{ km}
Step 2: Calculate Distance Traveled in the Next Hour
The car travels at a speed of 60 km/hr for the next hour.
- Speed in the next hour = 60 km/hr
- Time in the next hour = 1 hour
Distance traveled in the next hour is:
\text{Distance}_2 = 60 \text{ km/hr} \times 1 \text{ hr} = 60 \text{ km}
Step 3: Calculate Total Distance Traveled
The total distance traveled is the sum of the distances covered in the first and second hours.
\text{Total Distance} = \text{Distance}_1 + \text{Distance}_2
\text{Total Distance} = 40 \text{ km} + 60 \text{ km} = 100 \text{ km}
Step 4: Calculate Total Time Taken
The total time taken is the sum of the durations of the two parts of the journey.
\text{Total Time} = \text{Time}_1 + \text{Time}_2
\text{Total Time} = 1 \text{ hour} + 1 \text{ hour} = 2 \text{ hours}
Step 5: Calculate the Average Speed
Now, we use the average speed formula with the total distance and total time.
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\text{Average Speed} = \frac{100 \text{ km}}{2 \text{ hr}}
\text{Average Speed} = 50 \text{ km/hr}
So, the average speed of the car is 50 km/hr.
Summary of Average Speed Calculation
| Segment | Speed (km/hr) | Time (hr) | Distance (km = Speed $\times$ Time) |
|---|---|---|---|
| First Hour | 40 | 1 | 40 |
| Next Hour | 60 | 1 | 60 |
| Total | Time (hr) | Distance (km) | Average Speed (km/hr = Distance / Time) |
|---|---|---|---|
| Journey | 2 | 100 | 100 / 2 = 50 |
The calculated average speed matches one of the given options.
Revision Table: Speed, Distance, Time
| Concept | Formula | Units (Common) |
|---|---|---|
| Speed | $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ | km/hr, m/s, mph |
| Distance | $\text{Distance} = \text{Speed} \times \text{Time}$ | km, meters, miles |
| Time | $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ | hours, seconds |
| Average Speed | $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$ | km/hr, m/s, mph |
Additional Information on Average Speed vs. Average Velocity
It is important to distinguish between average speed and average velocity.
- Average Speed: This is a scalar quantity defined as the total distance covered divided by the total time taken. It does not consider the direction of motion.
- Average Velocity: This is a vector quantity defined as the total displacement divided by the total time taken. Displacement is the change in position from the starting point to the ending point, considering direction.
In this problem, assuming the car travels in a straight line in the same direction, the total distance is equal to the magnitude of the total displacement. Therefore, the average speed calculated here would be equal to the magnitude of the average velocity. However, if the car had changed direction, the total distance and displacement would be different, leading to different values for average speed and average velocity.
When different speeds are maintained for different time intervals, the average speed is a time-weighted average of the speeds, calculated as shown in the steps above.
Important Questions from Partial Speed
A train having length 210 metres takes 25 seconds to cross a 540 metres long bridge. How much time will the train take to cross a 630 metres long bridge?
A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1.5 km / hr and Y walks with a uniform speed of 1 km / hr in the first hour, with a uniform speed of 1.25 km / hr in the second hour and with a uniform speed of 1.5 km / hr in the third hour and so on.
Which of the following is / are correct?
1. They take 5 hours to meet.
2. They meet midway between A and B.
Select the correct answer using the code given below:
The speed of a train is 120 kmph. What is the distance covered by it in 15 minutes?
I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways ?
Karan had covered two third of a certain distance when his car had a breakdown. He parked it and covered the remaining distance on foot. His time of travel on foot was 9 times his time of travel on car. What is the ratio of his walking speed with respect to his car’s speed?
