Question

Тіло, що рухається рівноприскорено, змінює своє положення за законом х = - 20t + 15t2. Визначити початкову швидкість, прискорення та початкову координату тіла.​

Answer 1

Ответ:

vo= -20 м/с

a=30 м/с²

хо=0 м

Объяснение:

x(t)=xo+vo*t+a*t²/2

===========================

Answer 2

Ответ:

Объяснение:

Запишем уравнение движения в общем виде:

x(t) = x₀ + V₀·t + a·t²/2

Заданное уравнение:

x(t) = - 20·t + 15·t²/2

Тогда:

Начальная координата тела:

x₀ = 0 м

Начальная скорость:

V₀ = - 20 м/с

Ускорение:

a = 30 м/с²

Answer 3

Problem Statement

We are given the equation of motion for a body moving with constant acceleration: x = -20t + 15t^2. We need to determine the initial velocity, acceleration, and initial position of the body.

Solution

To solve this problem, we need to differentiate the equation of motion with respect to time to find the velocity and acceleration functions. Let's go step by step.

Finding the Velocity Function

To find the velocity function, we differentiate the equation of motion with respect to time (t):

v = dx/dt

Differentiating the equation x = -20t + 15t^2 with respect to t, we get:

v = -20 + 30t

So, the velocity function is given by v = -20 + 30t.

Finding the Acceleration Function

To find the acceleration function, we differentiate the velocity function with respect to time (t):

a = dv/dt

Differentiating the equation v = -20 + 30t with respect to t, we get:

a = 30

So, the acceleration function is constant and given by a = 30.

Finding the Initial Velocity

The initial velocity (v0) is the value of the velocity function at time t = 0. Substituting t = 0 into the velocity function v = -20 + 30t, we get:

v0 = -20 + 30(0) = -20

Therefore, the initial velocity of the body is v0 = -20.

Finding the Initial Position

The initial position (x0) is the value of the position function at time t = 0. Substituting t = 0 into the equation of motion x = -20t + 15t^2, we get:

x0 = -20(0) + 15(0)^2 = 0

Therefore, the initial position of the body is x0 = 0.

Summary

Based on the given equation of motion x = -20t + 15t^2, we have determined the following: - Initial velocity: v0 = -20 - Acceleration: a = 30 - Initial position: x0 = 0

Please let me know if there is anything else I can help you with!