Question

Зависимость координаты материальной точки от времени описывается уравнением (x - в метрах, t - в секундах). Тогда материальная х(t) = 3t - 6t^2 точка движется с ускорением, проекция аx которого на ось Ох равна...(чему?)

Answer 1

Ускорение вычислим как вторую производную от координаты х по времени:
а=х" =-12 м/с²
Поэтому, проекция ускорения на ось х отрицательна и равна -12 м/с²

Answer 2

Equation of Motion

The equation describing the position of a material point in terms of time is given by x(t) = 3t - 6t^2.

Acceleration of the Material Point

The acceleration of the material point, which is the projection of the acceleration onto the x-axis, can be found by taking the second derivative of the position function with respect to time. In this case, the acceleration a_x is given by the second derivative of the position function: a_x = d^2x/dt^2 = -12 m/s^2.

The negative sign indicates that the acceleration is directed opposite to the positive direction of the x-axis.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.