Question

во время тренировки на стадионе спортсмен пробежал 2 круга с разной скоростью v1 5 и v2 7,5 м/с. Какова средняя скорость спортсмена?​

Answer 1

Ответ:

• Средняя скорость спортсмена равна $\boldsymbol{\langle v \rangle}=\boldsymbol{6}$ м/с

Объяснение:

Дано:

S - весь путь

$\displaystyle S_1=S_2=\frac{S}{2}$

$v_1=5$ м/с

$v_2=7,5$ м/с

Найти: $\langle v \rangle$ - ?

Решение:

Среднепутевая скорость = весь путь / всё время.

Тогда $\displaystyle \boldsymbol{\langle v \rangle}=\frac{S_1+S_2}{t_1+t_2} =\frac{\frac{S}{2} +\frac{S}{2} }{\frac{S_1}{v_1}+\frac{S_2}{v_2} } =\frac{S}{\frac{S}{2v_1}+\frac{S}{2v_2} } =\frac{S}{\frac{S}{2} (\frac{1}{v_1}+\frac{1}{v_2} )} =\frac{2}{\frac{v_1+v_2}{v_1v_2} } =\frac{2v_1v_2}{v_1+v_2}$ (данную выведенную формулу можно использовать только в том случае, когда первая половина пути $S_1$ была преодолена со скоростью $v_1$, а вторая половина пути $S_2$ - со скоростью $v_2$).

Итак, средняя скорость спортсмена: $\displaystyle \boldsymbol{\langle v \rangle}=\frac{2v_1v_2}{v_1+v_2}=\frac{2\cdot 5\cdot 7,5}{5+7,5} =\boldsymbol{6}$ м/с.

Answer 2

Calculating Average Speed of the Athlete

To calculate the average speed of the athlete, we can use the formula:

Average Speed = Total Distance / Total Time

In this case, the athlete ran 2 laps at different speeds: v1 = 5 m/s and v2 = 7.5 m/s.

We can calculate the average speed using the given speeds.

Calculation

The total distance covered by the athlete is the same for both laps, as the athlete ran the same distance for each lap.

Let's denote the total distance covered by the athlete as "d" and the time taken for each lap as "t1" and "t2" respectively.

The total time taken for both laps is the sum of the time taken for each lap.

The time taken for each lap can be calculated using the formula:

Time = Distance / Speed

For the first lap: t1 = d / v1

For the second lap: t2 = d / v2

The total time taken for both laps: Total Time = t1 + t2

Substituting the values of t1 and t2, we get: Total Time = (d / v1) + (d / v2)

Now, we can calculate the average speed using the formula: Average Speed = Total Distance / Total Time

Let's proceed with the calculations.