Question

Велосипедист проехал первую половину пути со скоростью 6м/c, а вторую половину пути - со скоростью V2.Как велика эта скорость, если известно, что средняя скорость его движения на всем пути равна 4.8м/c ?

Answer 1

Дано V1 = 6 м/с   Vср=4,8 м/с  S1=S2=0,5*S     V2 - ?
Vср = S/t   - основная формула
t1 = 0,5*S/V1
t2=0,5*S/V2
Vср = S/(0,5*S/V1  +0,5*S/V2)
Vcр = 2*V1*V2/(V1 +V2)
далее решаем уравнение и получаем

V2= Vср*V1/(2V1-Vср)=4.8*6/(12-4.8)=4 м\с
100% гарантии

Answer 2

Problem Analysis

We are given that a cyclist traveled the first half of the distance at a speed of 6 m/s and the second half of the distance at a speed of V2. We need to find the value of V2 if the average speed of the cyclist for the entire distance is 4.8 m/s.

Solution

Let's assume the total distance traveled by the cyclist is D. Since the cyclist traveled the first half of the distance at a speed of 6 m/s, the time taken to cover the first half of the distance is D/2 / 6 = D/12 seconds. Similarly, the time taken to cover the second half of the distance is D/2 / V2 = D/(2V2) seconds.

The average speed of the cyclist for the entire distance is given by the formula:

Average Speed = Total Distance / Total Time

We are given that the average speed is 4.8 m/s. Substituting the values, we get:

4.8 = D / (D/12 + D/(2V2))

Simplifying the equation, we get:

4.8 = 1 / (1/12 + 1/(2V2))

To solve for V2, we can cross-multiply and solve the resulting equation.

Calculation

Let's solve the equation to find the value of V2.

1 / (1/12 + 1/(2V2)) = 4.8

Multiplying both sides by (1/12 + 1/(2V2)), we get:

1 = 4.8 * (1/12 + 1/(2V2))

Expanding the right side of the equation, we get:

1 = 4.8/12 + 4.8/(2V2)

Simplifying further, we get:

1 = 0.4 + 2.4/V2

Subtracting 0.4 from both sides, we get:

0.6 = 2.4/V2

Cross-multiplying, we get:

0.6 * V2 = 2.4

Dividing both sides by 0.6, we get:

V2 = 2.4 / 0.6

V2 = 4 m/s

Answer

The value of V2, the speed at which the cyclist traveled the second half of the distance, is 4 m/s.

Verification

To verify the answer, let's calculate the average speed using the given values:

Average Speed = Total Distance / Total Time

Total Distance = D Total Time = (D/12) + (D/(2*4))

Average Speed = D / ((D/12) + (D/8)) = D / (5D/24) = 24 / 5 = 4.8 m/s

The calculated average speed matches the given average speed, which confirms that the answer is correct.