Differential Calculus - Rectilinear Motion

RECTILINEAR MOTION

It is a particle's motion along a straight line path. The motion of the particle was perfectly characterized by an equation of the form s=f(t), also known as the equation of motion, where t>=0 is the time and is the displacement of the particle at any given time, measured from a selected fixed point in its path known as the reference point.

The chosen reference point is typically the initial position of the particle at time zero (t = 0). The equations below can be used to calculate the particle's velocity (v) and acceleration (a) at time t.

HORIZONTAL RECTILINEAR MOTION

This is motion of the particle is along a horizontal straight line. Since displacement, velocity and acceleration are all vector quantities, the following are the sign conventions:

• If s > 0 , right beside the reference point the particle is located.
• If s < 0 , left beside the reference point, the particle is located. 
• If v > 0 , the particle is moving in an increasing direction. s (moving to the right away from the reference point) 
• If v < 0 ,the particle is moving in an decreasing direction. s (moving to the left, towards or away from the reference point)
• if v = 0, the particle is at rest at that particular time
• If a > 0 , velocity is increasing
• If a < 0 , velocity is decreasing which means the particle is decelerating 

VERTICAL RECTILINEAR MOTION

A good illustration of a vertical rectilinear motion is free-fall motion. The moving particle, which is referred to as a freely falling body, is only influenced by its weight, and air resistance is considered to be negligible, It's acceleration is due to gravity.

The first two values are rounded-off to the nearest integer for computational convenience. For s and v , the following sign convention applies:

• If s > 0 , the particle is above the reference point
• if s < 0, the particle is below the reference point
• if v < 0, the particle is moving in upward direction
• if v > 0, the particle is moving in downward direction