Physics Theories/Motion Theory

Motion Theory

Motion refers to the movement of an object from one position to another position

If there is a Force F that makes an object of Mass m to move a Distance s within Time t Then the motion can be characterized by

Speed

The ratio of Distance over Time gives Speed of Motion
$v = \frac{s}{t}$

Acceleration

The ratio of Speed over time gives Acceleration of the motion
$a = \frac{v}{t}$

Distance

Distance travels of the motion is defined as the product of Mass times Acceleration
S = v t = a t2

Force

Force causing the Motion
F = m a = m v / t = p / t

Work Done

Work done by the force is the product of the Force and the Distance travel
W = F s F v t = p v

Energy

Work done by the force is the product of the Force and the Distance travel
$E = \frac{W}{t} = \frac{F s}{t} = F v = p a$

Linear Motion

Linear Motion is any motion moving in a straight line without changing it's direction . For instance, Linear Motion with constant speed over time , linear Motion with changing speed over time

Linear Motion with constant speed over time

For any Linear Motion that has constant speed at all time can be expressed as

v(t) = V

Linear Motion with changing speed over time

For any Linear Motion travels with different speed at different time v1 at t1 and v at t

The Change in Speed . ∆v = $v - v_1$
The Change in Time . ∆t = $t - t_1$
The ratio of Change in Speed over Change in Time gives the Accelerarion of the motion
a = ∆v / ∆t = $\frac{v - v_1}{t - t_1}$
∆v = a ∆t
v(t) = a t if ∆v = v , ∆t = t
a = $\frac{v - v_1}{t - t_1}$
$v = v_1 + a (t - t_1)$
$v_1 = v - a (t - t_1)$
$v_2 = v_1$ a = 0 . Linear motion with constant velocity
$v_2 > v_1$ a > 0 . Linear motion with increasing velocity
$v_2 < v_1$ a < 0 . Linear motion with decreasing velocity

Non - Linear Motion

For any Non linear motion v(t) that does not travel in a straight line with changing direction

Characteristics Symbol Calculus Equation
Speed v $\frac{ds(t)}{dt}$
Accelleration a $\frac{dv(t)}{dt} = \frac{d^2s}{dt^2}$
Distance s $\int v(t) dt$
Force F $m \frac{dv(t)}{dt}$
Work W $\frac {F}{t} \int v(t)dt$
Pressure P $\frac{ds(t)}{dt}$
Impulse Fm $m t \frac{dv(t)}{dt}$
Momentum mv $m \frac{ds(t)}{dt}$
Energy E $F \int v(t) dt$

Summary

For any motion travels a Distance in Time caused by a Force has the following characters

Characteristics Symbol Mathematic Formula Unit
Speed v $\frac{s}{t}$ = a t $\frac{m}{s}$
Accelleration a $\frac{v}{t}$ = $\frac{s}{t^2}$ $\frac{m}{s^2}$
Distance s v t = a t2 m
Force F m a kg $\frac{m}{s}$
Work W F s kg $\frac{m^2}{s}$
Pressure P $\frac{F}{A}$ kg $\frac{m}{s^3}$
Impulse Fm F t kg $\frac{m}{s}$
Momentum mv m v kg $\frac{m}{s}$
Energy E $\frac{W}{t}$ = $F \frac{s}{t}$ = F v kg $\frac{m^2}{s}$

For any non linear motion v(t)

Characteristics Symbol Calculus Equation
Speed v $\frac{ds(t)}{dt}$
Accelleration a $\frac{dv(t)}{dt} = \frac{d^2s}{dt^2}$
Distance s $\int v(t) dt$
Force F $m \frac{dv(t)}{dt}$
Work W $\frac {F}{t} \int v(t)dt$
Pressure P $\frac{ds(t)}{dt}$
Impulse Fm $m t \frac{dv(t)}{dt}$
Momentum mv $m \frac{ds(t)}{dt}$
Energy E $F \int v(t) dt$

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