Question

Мандрівник сходив на гору зі швидкістю 1 км/год, а потім спускався назад зі швидкістю 4 км/год. Яка середня шляхова швидкість на всьому шляху? яка векторна середня швидкість?

Answer 1

 можно воспользоваться формулой 

Vср.=(2V1 * V2) :(V1 +V2)  =( 2*1 * 4): (1+4)= 8/5 =1,6 км/год

Answer 2

Calculating Average Speed and Average Velocity

To calculate the average speed and average velocity of the traveler, we can use the following formulas:

1. Average Speed: - Average speed is calculated as the total distance traveled divided by the total time taken.

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

2. Average Velocity: - Average velocity is calculated as the displacement (change in position) divided by the total time taken.

\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}} \]

Given: - Speed uphill = 1 km/h - Speed downhill = 4 km/h

Calculating Average Speed

The average speed can be calculated using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

The traveler covers the same distance uphill and downhill, so the total distance is twice the distance of either the uphill or downhill journey.

The time taken for the uphill journey is the same as the time taken for the downhill journey.

Therefore, the average speed is the arithmetic mean of the uphill and downhill speeds.

The average speed is calculated as:

\[ \text{Average Speed} = \frac{1 \, \text{km/h} + 4 \, \text{km/h}}{2} = \frac{5 \, \text{km/h}}{2} = 2.5 \, \text{km/h} \]

The average speed for the entire journey is 2.5 km/h.

Calculating Average Velocity

The average velocity can be calculated using the formula:

\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}} \]

The displacement for the entire journey is zero, as the traveler ends up at the same position as the starting point.

Therefore, the average velocity for the entire journey is also zero.

The average velocity for the entire journey is 0 km/h.

These calculations show that the average speed for the entire journey is 2.5 km/h, while the average velocity for the entire journey is 0 km/h.