The kinematic law of train motion along the Ox axis has the form: x = 0.2t ^ 2. Is the train accelerating

| September 9, 2021 | education

The kinematic law of train motion along the Ox axis has the form: x = 0.2t ^ 2. Is the train accelerating or slowing down? Determine the projection of the initial velocity and acceleration. Write down the equation of the projection of the speed on the Ox axis. Plot projections of acceleration and speed.

Basic path equation: s = x = v0 * t + a * t ^ 2/2 = 0.2 * t ^ 2. (1). Whence it is seen that at the initial moment t = 0, v0 = 0 m / s.

Velocity projection equation:

v = x ′ = (at ^ 2) ′ = 0, 4 * t, whence it is clear that v (0) = 0.

Since a * t ^ 2/2 = 0.2 (seen from (1), then a = 0.2 * 2 = 0.4 m / s ^ 2. Since a = 0.4> 0, then the motion uniformly accelerated, the train accelerates.

Construction of graphs: acceleration a = 0.4 = const – straight line, parallel to OX, at the level of y = 0.4.

The speed graph is a straight line from point (0; 0) to point (x = 1; y = 0.4).



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