Question

По заданному уравнению движения точки S = 25 + 1,5t + 6t2 определите вид движения и без расчетов, используя законы движения точки, ответьте, чему равны начальная скорость и ускорение.

Answer 1

Равноускоренное прямолинейное движение.
задается уравнением
х0 + v0t + at²\2.
25 + 1,5t + 6t²
теперь просто смотрим на уравнение.
v0 = 1.5
a = 6*2=12

Answer 2

Equation of Motion and Determining the Type of Motion

The equation of motion given is S = 25 + 1.5t + 6t^2, where S represents the displacement of a point, t represents time, and the coefficients represent the respective terms in the equation.

To determine the type of motion without calculations, we can analyze the equation. The equation is a quadratic equation in terms of time (t), which means it represents a parabolic curve. The presence of the term t^2 indicates that the motion is not linear but rather a curved path.

Based on this information, we can conclude that the type of motion described by the equation is curvilinear motion.

Initial Velocity and Acceleration

To determine the initial velocity and acceleration, we need to differentiate the equation of motion with respect to time (t).

Differentiating the equation S = 25 + 1.5t + 6t^2 with respect to t, we get:

dS/dt = 1.5 + 12t

The derivative of displacement with respect to time gives us the velocity (v) of the point. Therefore, the velocity equation is:

v = 1.5 + 12t

To find the initial velocity, we substitute t = 0 into the velocity equation:

v(0) = 1.5 + 12(0) = 1.5

Hence, the initial velocity of the point is 1.5 units per time.

To find the acceleration, we differentiate the velocity equation with respect to time:

dv/dt = 12

The derivative of velocity with respect to time gives us the acceleration (a) of the point. Therefore, the acceleration equation is:

a = 12

Hence, the acceleration of the point is 12 units per time squared.

In summary: - The type of motion described by the equation is curvilinear motion. - The initial velocity of the point is 1.5 units per time. - The acceleration of the point is 12 units per time squared.

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