Physics Theories/Motion Theory

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Motion Theory[edit]

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[edit]

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

Acceleration[edit]

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

Distance[edit]

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

Force[edit]

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

Work Done[edit]

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

Energy[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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

Periodic Motion[edit]

Spring's Oscillation[edit]

Pendulum's Oscillation[edit]

Summary[edit]

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

Reference[edit]

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