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

The calculated average speed matches one of the given options.

Revision Table: Speed, Distance, Time

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.