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
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
