Kinematics
Motion of a Particle
Particle is a term used to denote an object of point size. A system of particles which formed into appreciable size is termed as body. These terms may apply equally to the same object. The earth for example may be assumed as a particle in comparison with its orbit, whereas to an observer on the earth, it is a body with appreciable size. In general, a particle is an object whose size is so small in comparison to the size of its path.
Rectilinear Translation (Motion Along a Straight Line)
Motion with constant acceleration
$s = v_it + \frac{1}{2}at^2$
${v_f}^2 = {v_i}^2 + 2as$
Free-falling body
$h = \frac{1}{2}gt^2$
$v^2 = 2gh$
Note: From motion with constant acceleration, set vi = 0, vf = v, s = h, and a = g to get the free-fall formulas.
Motion with variable acceleration
$v = \dfrac{ds}{dt}$
$v \, dv = a \, ds$
Where
$s$ = distance
$h$ = height
$v$ = velocity
$v_i$ = initial velocity
$v_f$ = final velocity
$a$ = acceleration
$g$ = acceleration due to gravity (g = 9.81 m/s2 in SI = 32.2 ft/s2 in English)
$t$ = time
Note:
• $a$ is positive (+) if $v$ is increasing (accelerate).
• $a$ is negative (-) if $v$ is decreasing (decelerate).
• $g$ is positive (+) if the particle is moving downward.
• $g$ is negative (-)if the particle is moving upward.
Useful conversion factors:
| From | To | Multiply by |
| Kilometers per hour (kph) | Meter per second (m/sec) | 1 / 3.6 |
| Meter per second (m/sec) | Kilometers per hour (kph or km/hr) | 3.6 |
| Miles per hour (mph) | Feet per second (fps or ft/sec) | 22 / 15 |
| Feet per second (ft/sec) | Miles per hour (mph or mi/hr) | 15 / 22 |