Question

Тело начинает движение из состояния покоя с ускорением а=2 м/с2, после чего, двигаясь равномерно, проходит расстояние S=18 метров. Найти минимальное время (в секундах) всего движения.

Answer 1

18м÷2м/с=9с^2

9с^2=3с

ответ:3 с

Answer 2

Problem Analysis

We are given the following information: - The body starts moving from rest with an acceleration of a = 2 m/s^2. - The body then moves uniformly and covers a distance of S = 18 meters.

We need to find the minimum time it takes for the entire motion.

Solution

To find the minimum time for the entire motion, we can divide the motion into two parts: 1. The initial acceleration phase. 2. The uniform motion phase.

Let's calculate the time for each phase and then add them together to find the total time.

Phase 1: Initial Acceleration

During the initial acceleration phase, the body starts from rest and accelerates with an acceleration of a = 2 m/s^2. We need to find the time it takes for the body to cover a certain distance during this phase.

We can use the following kinematic equation to find the time taken during the initial acceleration phase:

S = ut + (1/2)at^2

Where: - S is the distance covered during the initial acceleration phase (unknown). - u is the initial velocity (0 m/s as the body starts from rest). - a is the acceleration (2 m/s^2). - t is the time taken during the initial acceleration phase (unknown).

Rearranging the equation, we get:

t = sqrt(2S/a)

Substituting the given values, we have:

t = sqrt(2 * 18 / 2) = sqrt(18) = 4.2426 seconds .

Phase 2: Uniform Motion

During the uniform motion phase, the body moves with a constant velocity. We need to find the time it takes for the body to cover the remaining distance after the initial acceleration phase.

The distance covered during the uniform motion phase is given by:

S = vt

Where: - S is the remaining distance to be covered (18 meters). - v is the constant velocity during the uniform motion phase (unknown). - t is the time taken during the uniform motion phase (unknown).

Rearranging the equation, we get:

t = S / v

Substituting the given values, we have:

t = 18 / v

Total Time

The total time for the entire motion is the sum of the time taken during the initial acceleration phase and the time taken during the uniform motion phase.

Total Time = Time for Initial Acceleration + Time for Uniform Motion

Total Time = 4.2426 seconds + 18 / v seconds

To find the minimum time, we need to find the minimum value of v. Since the body is moving uniformly, the minimum value of v is 0 (when the body comes to rest).

Therefore, the minimum total time for the entire motion is:

Total Time = 4.2426 seconds + 18 / 0 seconds = infinity

Since the body cannot cover the remaining distance in 0 seconds, the minimum total time for the entire motion is infinity.

Answer

The minimum total time for the entire motion is infinity.

Please let me know if I can help you with anything else.