Linear Motion

Linear motion (also called rectilinear motionis a motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types

1. Uniform linear motion with constant velocity or zero acceleration
2. Non uniform linear motion with variable velocity or non-zero acceleration
3. Instananeous linear motion with variable velocity or non-zero acceleration

The motion of a particle (a point-like object) along a line can be described by its position ${\displaystyle x}$, which varies with ${\displaystyle t}$ (time)

Uniform linear motion

For any linear motion follows a straight line travels at speed does not change with time . the speed of motion is called uniform speed

${\displaystyle v={\frac {distance}{time}}={\frac {s}{t}}}$

${\displaystyle a={\frac {v}{t}}}$

${\displaystyle s=vt}$

Non- uniform linear motion

For any motion follows a straight line travels at a changing speed change with changing time . Te speed of motion is called non uniform speed

${\displaystyle a={\frac {averagespeed}{averagetime}}={\frac {\Delta v}{\Delta t}}={\frac {v-v_{o}}{t-t_{o}}}}$

${\displaystyle v=v_{o}+a(t-t_{o})}$

${\displaystyle s=v_{o}t+at(t-t_{o})}$

Instantaneous linear motion

Speed at any time is called instantaneous speed can be found by differentiating the displacement with respect to time.

${\displaystyle \mathbf {v} =\lim _{\Delta t\to 0}{\Delta x \over \Delta t}}$ ${\displaystyle ={\frac {dx}{dt}}}$

Relative motion

Motion travels at speed relative to speed of light

${\displaystyle \gamma ={\sqrt {1-{\frac {v^{2}}{C^{2}}}}}}$

Reference

• Linear Motion
• Motion