Question

Первую треть пути тело двигалось со скоростью V1=20 м\с,вторую треть - со скоростью V2=12 м\с и последнюю треть - со скоростью V3=2 м\с.Определите среднюю скорость движения тела

Answer 1

Пусть весь путь, проделанный телом будет равен S. Тогда первую треть пути тело проделало за S/3V₁=S/20секунд, вторую треть за S/3V₂=S/12, а третью - за S/3V₃=S/2 секунды. Средняя скорость тела равна отношению всего пройденного пути к всему потраченному времени, таким образом
$V_{cp}= \frac{S}{\frac{1}{3}(\frac{S}{20}+\frac{S}{12}+\frac{S}{2}})= \frac{S}{ \frac{1}{3}(\frac{3S}{60}+\frac{5S}{60}+\frac{30S}{60})}=\frac{180S}{ 38S}= 4\frac{14}{19}$ или примерно 4,737
Ответ: средняя скорость тела 4,737 м/c

Answer 2

Calculation of Average Speed

To calculate the average speed of an object, we need to find the total distance traveled and the total time taken. In this case, the object traveled for three equal intervals, each with a different speed.

Let's assume the total distance traveled by the object is D.

The first third of the distance was covered at a speed of V1 = 20 m/s. The second third of the distance was covered at a speed of V2 = 12 m/s. The last third of the distance was covered at a speed of V3 = 2 m/s.

To find the average speed, we need to calculate the total time taken to cover the entire distance.

The time taken to cover the first third of the distance can be calculated using the formula:

Time1 = Distance1 / Speed1

Similarly, the time taken to cover the second and last thirds of the distance can be calculated using the formulas:

Time2 = Distance2 / Speed2 Time3 = Distance3 / Speed3

Since the distances covered in each interval are equal, we can assume that:

Distance1 = Distance2 = Distance3 = D/3

Now, let's calculate the time taken for each interval:

Time1 = (D/3) / V1 Time2 = (D/3) / V2 Time3 = (D/3) / V3

To find the total time taken, we add the times for each interval:

Total Time = Time1 + Time2 + Time3

Finally, we can calculate the average speed using the formula:

Average Speed = Total Distance / Total Time

Let's plug in the given values and calculate the average speed.