A truck travels 40 km in first hour and 50 km in second hour. What is the average speed of truck?
45 km/hr
Calculating Average Speed of a Truck
The question asks us to find the average speed of a truck that travels different distances in different hours.
Average speed is defined as the total distance traveled divided by the total time taken for the journey.
The formula for average speed is:
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
Step-by-Step Calculation
Let's break down the information given in the problem:
- Distance covered in the first hour: 40 km
- Time taken for the first part: 1 hour
- Distance covered in the second hour: 50 km
- Time taken for the second part: 1 hour
1. Calculate Total Distance
The total distance is the sum of the distances covered in each hour.
\(\text{Total Distance} = \text{Distance in hour 1} + \text{Distance in hour 2}\)
\(\text{Total Distance} = 40 \text{ km} + 50 \text{ km}\)
\(\text{Total Distance} = 90 \text{ km}\)
2. Calculate Total Time
The total time is the sum of the times taken for each part of the journey.
\(\text{Total Time} = \text{Time in hour 1} + \text{Time in hour 2}\)
\(\text{Total Time} = 1 \text{ hour} + 1 \text{ hour}\)
\(\text{Total Time} = 2 \text{ hours}\)
3. Calculate Average Speed
Now, we use the formula for average speed with the calculated total distance and total time.
\(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\)
\(\text{Average Speed} = \frac{90 \text{ km}}{2 \text{ hours}}\)
\(\text{Average Speed} = 45 \text{ km/hr}\)
Therefore, the average speed of the truck is 45 km/hr.
Revision Table: Speed, Distance, Time Concepts
| Concept | Definition | Formula | Units (Common) |
|---|---|---|---|
| Speed | Rate at which an object covers distance. | \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\) | m/s, km/hr, mph |
| Distance | Total path covered by an object. | \(\text{Distance} = \text{Speed} \times \text{Time}\) | meters, kilometers, miles |
| Time | Duration for which motion occurs. | \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) | seconds, minutes, hours |
| Average Speed | Total distance divided by total time. | \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\) | m/s, km/hr, mph |
Additional Information on Average Speed
It's important to distinguish between average speed and average velocity. While average speed is the total distance covered divided by total time, average velocity is the total displacement divided by total time.
In this problem, since the truck is moving in a straight line and we are considering the total distance, the calculation using total distance divided by total time gives the average speed.
If the truck had traveled 40 km east in the first hour and then 40 km west in the second hour, the total distance would be 80 km (40 + 40), total time would be 2 hours, and average speed would be 40 km/hr. However, the displacement would be 0 km (since it returned to the starting point), and the average velocity would be 0 km/hr.
In problems involving varying speeds over different time intervals or distances, always use the total distance and total time to find the average speed.
Important Questions from Speed Time and Distance
The average speed of a train is 180% of the average speed of a car. The car covers a distance of 990 km in 15 hours. The time taken (in hours) by the train to cover the distance of 891 km is:
If Rohit can cover a distance of 1188 km in 22 hours, then what is the speed of Rohit?
A train is moving at 72 km/hrs. The distance covers in 15 minutes by the train is:
If Sonu is driving a car at a speed of 20 m/s, then in how much time Sonu will cover a distance of 936 km?
A person crosses a 1600 m long street in 4 min. What is his speed (in km/h)?
