Question

Автомобиль проехал первую четверть времени со скоростью 72 км/ч, а оставшееся время со скоростью 15 м/с. Найти среднюю скорость за всё время движения.

Answer 1

Vcp=весь путь / всё время.

Пусть всё время движения  -  t

Тогда весь путь

S=S1 + S2=V1*t1 + V2*t2=20 * (t/4) + 15 * (3t/4)=

(5 + 45/4)*t=16 1/4 * t

Vcp=16,25*t / t=16,25 м/с  -  это ответ.

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72 км/ч=72*1000 м/3600 с=20 м/с.

Answer 2

Calculation of Average Speed

To find the average speed for the entire duration of the journey, we need to calculate the total distance traveled and the total time taken.

Let's assume the total time of the journey is t.

The car traveled the first quarter of the time, which is t/4, at a speed of 72 km/h. This means the distance covered in the first quarter is 72 * (t/4).

The remaining time is 3t/4, and the car traveled at a speed of 15 m/s during this time. To calculate the distance covered in the remaining time, we need to convert the speed from m/s to km/h. Since 1 m/s is equal to 3.6 km/h, the speed of 15 m/s is equal to 15 * 3.6 = 54 km/h. Therefore, the distance covered in the remaining time is 54 * (3t/4).

The total distance covered during the entire journey is the sum of the distances covered in the first quarter and the remaining time: 72 * (t/4) + 54 * (3t/4).

The total time taken for the journey is t.

To find the average speed, we divide the total distance by the total time:

Average Speed = Total Distance / Total Time

Substituting the values, we get:

Average Speed = (72 * (t/4) + 54 * (3t/4)) / t

Simplifying the equation, we have:

Average Speed = (18t + 162t) / (4t)

Average Speed = (180t) / (4t)

Average Speed = 45 km/h

Therefore, the average speed for the entire time of the journey is 45 km/h.