Motion along a line occurs when a particle moves along a line according to the equation f(t). The equation f(t) represents the position of the particle on the line at time t. F'(t) represents the velocity of the particle at time t, and f"(t) represents the acceleration of the particle.
Laws of Particle Motion at Any Instant
If the velocity is positive, then the particle is moving to the right and its distance is increasing. If the velocity is negative then it is moving to the left and its velocity is decreasing.
If the acceleration is positive then the velocity is increasing. If the acceleration is negative then the velocity is decreasing.
If the acceleration and velocity are both positive or both negative then the speed of the particle is increasing/ accelerating.
If the acceleration and velocity have opposite signs, then the speed of the particle is decreasing/ decelerating.
If the velocity is 0 and the acceleration is not 0, then the particle is reversing direction.
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