Question

Автомобиль трогается с места с ускорением 1м/с в тот момент когда мимо с постоянной скоростью 36км/ч проезжает трамвай. Через какой промежуток времени автомобиль догонит трамвай?

Answer 1

Составляем уравнение, исходя из того что равномерное перемещение трамвая равно равноускоренному перемещению автомобиля:  (конечно учтем, что 36 км/ч = 10 м/с)

$\frac{at^2}{2}=vt.$

Отсюда находим время:

$t=\frac{2v}{a}=\frac{2*10}{1}=\ 20\ c.$

Ответ: 20 с.

 

 

Answer 2

Calculating the Time to Catch Up to the Tram:

To calculate the time it takes for the car to catch up to the tram, we can use the formula: $$ \text{time} = \frac{\text{distance}}{\text{speed}} $$

The car is accelerating at 1 m/s, and the tram is traveling at a constant speed of 36 km/h. We need to convert the speed of the tram from km/h to m/s to ensure the units are consistent.

1. Convert the speed of the tram from km/h to m/s: - 36 km/h = 10 m/s

2. Calculate the time it takes for the car to catch up to the tram: - Let's denote the time as t.

- The distance the car travels while catching up to the tram can be calculated using the equation of motion: $$ \text{distance} = \text{initial velocity} \times \text{time} + \frac{1}{2} \times \text{acceleration} \times \text{time}^2 $$ - Here, the initial velocity of the car is 0 m/s (as it starts from rest), and the acceleration is 1 m/s^2.

- The distance the tram travels while the car is catching up can be calculated using the formula: $$ \text{distance} = \text{speed} \times \text{time} $$

- Equating the distances traveled by the car and the tram will give us the time it takes for the car to catch up to the tram.

3. Solve for the time t using the above information and the equations.

Let's calculate the time it takes for the car to catch up to the tram.