a bus travels from one point to another wuth a speed of 40km/h and returns with a speed of 60km/h.what is e average speed and average velocity of the bus?
Average Speed = (40+60)/2 = 50 km/h
To calculate the average speed and average velocity of the bus, we need to understand the definitions of speed and velocity.
1. Speed: Speed is the distance traveled per unit of time, irrespective of the direction of motion. It is calculated by dividing the total distance traveled by the total time taken.
2. Velocity: Velocity is the displacement (change in position) per unit of time, taking into account both the magnitude and direction of motion. It is calculated by dividing the total displacement by the total time taken.
Let's find the average speed and average velocity of the bus step-by-step:
1. Determine the distance traveled in one direction: Let's assume the distance traveled from point A to point B is D km.
2. Calculate the time taken for the first leg of the journey: Since the speed is given as 40 km/h, the time taken for the first leg is D/40 hours.
3. Determine the distance traveled in the return journey: As the bus is traveling back to the starting point, the distance traveled will be the same, i.e., D km.
4. Calculate the time taken for the return journey: Since the speed is given as 60 km/h, the time taken for the return journey is D/60 hours.
5. Calculate the total distance traveled: The total distance traveled is 2D km (D km in one direction + D km in the return journey).
6. Calculate the total time taken: The total time taken is (D/40 + D/60) hours.
Now we can calculate the average speed and average velocity using the above data:
Average Speed = Total Distance / Total Time
= (2D km) / (D/40 + D/60) hours
Simplifying this expression further:
Average Speed = (2D km) / [(3D + 2D)/120] (taking the least common multiple as 120)
= 240D km / (5D + 6D)
= 240D km / 11D
= 21.82 km/h
Therefore, the average speed of the bus is 21.82 km/h.
Average Velocity = Total Displacement / Total Time
In this case, the total displacement for the entire journey would be zero because the bus starts and ends at the same point. So, the average velocity would be zero.
Therefore, the average velocity of the bus is zero.