Question

Задача No3. Рівняння руху тіла має вигляд: х = 5 + 10t + 2t². Всі величини в рівнянні вказані в системі СІ. Яка початкова швидкість руху тіла? Куди напрямлене прискорення? Який його модуль?​

Answer 1

Ответ:

1.10

Объяснение:

Answer 2

Equation of Motion

The equation of motion for the given problem is given by:

x = 5 + 10t + 2t²

where: - x is the position of the body - t is the time

Finding the Initial Velocity

To find the initial velocity of the body, we need to differentiate the equation of motion with respect to time (t). The derivative of the position function with respect to time gives us the velocity function.

Differentiating the equation of motion, we get:

v = dx/dt = d(5 + 10t + 2t²)/dt = 10 + 4t

The initial velocity (v₀) is the value of velocity when time (t) is equal to zero. Substituting t = 0 into the velocity equation, we can find the initial velocity:

v₀ = 10 + 4(0) = 10

Therefore, the initial velocity of the body is 10 m/s.

Direction and Magnitude of Acceleration

To find the direction and magnitude of acceleration, we need to differentiate the velocity function with respect to time (t). The derivative of the velocity function with respect to time gives us the acceleration function.

Differentiating the velocity function, we get:

a = dv/dt = d(10 + 4t)/dt = 4

The acceleration (a) is a constant value of 4 m/s². Since the acceleration is positive, it indicates that the body is undergoing uniform acceleration in the positive direction.

Therefore, the initial velocity of the body is 10 m/s, and the acceleration is 4 m/s² in the positive direction.