Question

Поезд, двигаясь равноускоренно в течение 10 с, увеличил скорость с 36 км/ч до 54 км/ч. В течение следующих 0,3 мин он двигался равномерно. Найти модуль вектора перемещения.

Answer 1

395 окончательный ответ

Answer 2

Calculation of Displacement Vector

To find the displacement vector, we need to calculate the total displacement during the given time period. Let's break down the problem step by step:

1. The train initially has a speed of 36 km/h. 2. Over a period of 10 seconds, the train accelerates and increases its speed to 54 km/h. 3. After that, the train moves at a constant speed for the next 0.3 minutes.

To calculate the displacement vector, we can divide the problem into two parts: the initial acceleration phase and the constant speed phase.

# Initial Acceleration Phase

During the initial acceleration phase, the train's speed increases from 36 km/h to 54 km/h over a period of 10 seconds. To calculate the displacement during this phase, we can use the formula:

Displacement = Initial Velocity * Time + (1/2) * Acceleration * Time^2

In this case, the initial velocity is 36 km/h, the time is 10 seconds, and the acceleration can be calculated using the formula:

Acceleration = (Final Velocity - Initial Velocity) / Time

Substituting the values into the formulas, we get:

Acceleration = (54 km/h - 36 km/h) / 10 s

Now, we can calculate the displacement during the initial acceleration phase.

# Constant Speed Phase

During the constant speed phase, the train moves at a constant speed of 54 km/h for the next 0.3 minutes. To calculate the displacement during this phase, we can use the formula:

Displacement = Velocity * Time

In this case, the velocity is 54 km/h and the time is 0.3 minutes.

Now, let's calculate the displacement during the constant speed phase.

# Total Displacement

To find the total displacement, we need to add the displacements from the initial acceleration phase and the constant speed phase.

Now, let's calculate the total displacement.

Calculation Steps

1. Calculate the acceleration: - Acceleration = (54 km/h - 36 km/h) / 10 s

2. Calculate the displacement during the initial acceleration phase: - Displacement_initial = 36 km/h * 10 s + (1/2) * Acceleration * (10 s)^2

3. Calculate the displacement during the constant speed phase: - Displacement_constant = 54 km/h * 0.3 min

4. Calculate the total displacement: - Total Displacement = Displacement_initial + Displacement_constant

Now, let's calculate the displacement vector.

Calculation

1. Calculate the acceleration: - Acceleration = (54 km/h - 36 km/h) / 10 s = 1.8 m/s^2 2. Calculate the displacement during the initial acceleration phase: - Displacement_initial = 36 km/h * 10 s + (1/2) * 1.8 m/s^2 * (10 s)^2 = 180 m + 90 m = 270 m 3. Calculate the displacement during the constant speed phase: - Displacement_constant = 54 km/h * 0.3 min = 54 km/h * 0.3 min * (1000 m / 1 km) * (1 h / 60 min) = 270 m 4. Calculate the total displacement: - Total Displacement = Displacement_initial + Displacement_constant = 270 m + 270 m = 540 m

Therefore, the magnitude of the displacement vector is 540 meters.