Motion of Paricle

Motion of a Particle

Paricle 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 velocity (uniform motio)

s=vt

Motion with constant acceleration

vf=vi+at

s=vit+12at2

vf2=vi2+2as

Free-falling body

v=gt

h=12gt2

v2=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

a=dvdt

v=dsdt

vdv=ads

Where

s = distance

h = height

v = velocity

vi = initial velocity

vf = 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 |