A car travels one third distance on a straight road with a velocity of 10 km/hr, nest one third distance with velocity 20km/hr and the last journey with 60km/hr.what is the average velocity of the car in the whole journey?
Mean = ∑x/n
(10+20+60)/3 = ?
To find the average velocity of the car for the entire journey, we need to consider the distances traveled and the time taken at each velocity.
Let's assume the total distance traveled by the car is D.
The car travels one third of the total distance at a velocity of 10 km/hr. This means it covers (1/3) * D distance at 10 km/hr. The time taken for this part of the journey can be calculated using the formula:
Time = Distance / Velocity
So, the time taken for the first part of the journey is (1/3) * D / 10.
Similarly, the car travels the next one third of the total distance at a velocity of 20 km/hr. This means it covers (1/3) * D distance at 20 km/hr. The time taken for this part of the journey is (1/3) * D / 20.
Finally, the car travels the last one third of the total distance at a velocity of 60 km/hr. This means it covers (1/3) * D distance at 60 km/hr. The time taken for this part of the journey is (1/3) * D / 60.
To calculate the average velocity, we need to divide the total distance traveled by the total time taken:
Average Velocity = Total Distance / Total Time
Total Distance = D
Total Time = (1/3) * D / 10 + (1/3) * D / 20 + (1/3) * D / 60
Simplifying the equation:
Total Time = D/30 + D/60 + D/180
Total Time = (6D + 3D + D) / 180
Total Time = 10D / 180
Total Time = D / 18
So, the average velocity can be calculated as:
Average Velocity = D / (D / 18)
Average Velocity = 18 km/hr
Therefore, the average velocity of the car over the entire journey is 18 km/hr.