Kinematics

Path, time, speed
$$S = v\cdot t$$
S - path
v - speed (velocity)
t - time
Find   It is known that:
      =   
Calculate 'S'

Uniform motion
$$x = x_0+v\cdot t$$
x - coordinate
x0 - original (initial) coordinate
v - speed (velocity)
t - time
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      =   
Calculate 'x'

Uniformly accelerated motion: acceleration
$$a = \frac{v-v_0}{t}$$
a - acceleration
v - speed (velocity)
v0 - initial speed
t - time
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      =   
Calculate 'a'

Uniformly accelerated motion: speed
$$v = v_0+a\cdot t$$
v - speed (velocity)
v0 - initial speed
a - acceleration
t - time
Find   It is known that:
      =   
Calculate 'v'

Uniformly accelerated motion: path
$$s = v\cdot t+\frac{a\cdot t^{2}}{2}$$
s - path
v - speed (velocity)
t - time
a - acceleration
Find   It is known that:
      =   
Calculate 's'

Uniformly accelerated motion: coordinate
$$x = x_0+v\cdot t+\frac{a\cdot t^{2}}{2}$$
x - coordinate
x0 - original (initial) coordinate
v - speed (velocity)
t - time
a - acceleration
Find   It is known that:
      =   
Calculate 'x'

Height of a body thrown vertically upward (downward)
$$h = h_0+v_0\cdot t-\frac{g\cdot t^{2}}{2}$$
h - height
h0 - initial height
v0 - initial speed
t - time
g - free fall acceleration
Find   It is known that:
      =   
Calculate 'h'

Speed of a body thrown vertically upward (downward)
$$v = v_0-g\cdot t$$
v - speed (velocity)
v0 - initial speed
g - free fall acceleration
t - time
Find   It is known that:
      =   
Calculate 'v'

Speed, acceleration, time
$$v = a\cdot t$$
v - speed (velocity)
a - acceleration
t - time
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      =   
Calculate 'v'

Free-fall velocity
$$v = g\cdot t$$
v - speed (velocity)
g - free fall acceleration
t - time
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      =   
Calculate 'v'

Centripetal acceleration
$$a = \frac{v^{2}}{R}$$
a - centripetal acceleration
v - speed (velocity)
R - radius
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      =   
Calculate 'a'

Angular speed (velocity)
$$\omega = \frac{\phi}{t}$$
ω - angular speed (velocity)
φ - angle
t - time
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      =   
Calculate 'ω'

Uniform circular motion
$$l = R\cdot \phi$$
l - circular arc length
R - radius
φ - angle
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      =   
Calculate 'l'

Uniform circular motion: linear speed
$$v = R\cdot \omega$$
v - linear speed (velocity)
R - radius
ω - angular speed (velocity)
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      =   
Calculate 'v'

Rotation period
$$T = \frac{t}{N}$$
T - period
t - time
N - number of rotations
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      =   
Calculate 'T'

Rotation period
$$T = \frac{2\cdot \pi\cdot R}{v}$$
T - period
R - radius
v - linear speed (velocity)
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      =   
Calculate 'T'

Rotation period
$$T = \frac{2\cdot \pi}{\omega}$$
T - period
ω - angular speed (velocity)
Find   It is known that:
      =   
Calculate 'T'

Centripetal acceleration
$$a = \frac{4\cdot \pi^{2}\cdot R}{T^{2}}$$
a - centripetal acceleration
R - radius
T - rotation period
Find   It is known that:
      =   
Calculate 'a'

Centripetal acceleration
$$a = 4\cdot \pi^{2}\cdot R\cdot n^{2}$$
a - centripetal acceleration
R - radius
n - rotation frequency
Find   It is known that:
      =   
Calculate 'a'

Rotation frequency
$$n = \frac{1}{T}$$
n - rotation frequency
T - rotation period
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      =   
Calculate 'n'

Centripetal acceleration
$$a = \omega^{2}\cdot R$$
a - centripetal acceleration
ω - angular speed (velocity)
R - radius
Find   It is known that:
      =   
Calculate 'a'

Coordinate (range) of projectile launched at an angle
$$x = v_0\cdot t\cdot cos(\alpha)$$
x - coordinate
v0 - initial speed
t - time
α - angle
Find   It is known that:
      =   
Calculate 'x'

Flight height of projectile launched at an angle
$$y = v_0\cdot t\cdot sin(\alpha)-\frac{g\cdot t^{2}}{2}$$
y - coordinate (flight height)
v0 - initial speed
t - time
g - free fall acceleration
α - angle
Find   It is known that:
      =   
Calculate 'y'

Vertical velocity (speed) of projectile launched at an angle
$$v_{y} = v_0\cdot sin(\alpha)-g\cdot t$$
v_y - vertical speed (velocity)
v0 - initial speed
α - angle
g - free fall acceleration
t - time
Find   It is known that:
      =   
Calculate 'v_y'

Maximum height of projectile launched at an angle
$$h_{max} = \frac{v_0^{2}\cdot sin(\alpha)^{2}}{2\cdot g}$$
h_max - maximum height
v0 - initial speed
α - angle
g - free fall acceleration
Find   It is known that:
      =   
Calculate 'h_max'

Total flight time of projectile launched at an angle
$$t = \frac{2\cdot v_0\cdot sin(\alpha)}{g}$$
t - time
v0 - initial speed
α - angle
g - free fall acceleration
Find   It is known that:
      =   
Calculate 't'

Maximum range of projectile launched at an angle
$$s_{max} = \frac{v_0^{2}}{g}$$
s_max - maximum range
v0 - initial speed
g - free fall acceleration
Find   It is known that:
      =   
Calculate 's_max'

Coordinate (range) of projectile launched horizontally
$$x = x_0+v\cdot t$$
x - coordinate (range)
x0 - original (initial) coordinate
v - speed (velocity)
t - time
Find   It is known that:
      =   
Calculate 'x'

Flight height of projectile launched horizontally
$$y = y_0-\frac{g\cdot t^{2}}{2}$$
y - coordinate (flight height)
y0 - initial coordinate (height)
g - free fall acceleration
t - time
Find   It is known that:
      =   
Calculate 'y'

Total flight time of projectile launched horizontally
$$t_{max} = \sqrt {\frac{2\cdot h}{g}}$$
t_max - maximum amount of time
h - height
g - free fall acceleration
Find   It is known that:
      =   
Calculate 't_max'

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