R² = v_{1^{2 +}} v_2²

θ = tan^-1(opposite/adjacent)

R² = v₁² + v₂² -- 2 v₁ v₂ cos θ

R/sinθ_R = v₂/sinθ v₂

Slope = Velocity

Plateau = Stopped

Zero = Origin

Change Slope Sign = Change Direction

Displacement = Last Position

+ Slope = Forward

- Slope = Backwards

Slope = Acceleration

Plateau = Constant Velocity

Zero = Stopped

Pass Origin = Change Directions

Displacement = Add up distances

Area under the line segment = Distance

Total distance = ∑lDistancesl

Plateau = Constant Acceleration

+ Accelerating

-- Decelerating

0 = Nonaccelerating = Constant Velocity

v_ave.= v_i+v_f /2

a = (v_f - v_l)/ t

v_f = v_i + at

acceleration = gravity = 9.8 m/s²

Assume that:

v_yi = 0 m/s   v_yf = gt   d_y = ½gt²

v_f² = 2gd_y   t = (2d_y/g)^½

v_x = Rcosθ    v_y = Rsinθ

t_flight = 2v_y/g    t_max = t_flight/2

range = d_y = v_xt

max height reached midway: d_ymax= v_it_max+½at_max²

solve v_x, v_y and t in terms

of R and plug into v_x=d_x/t

solve for R

solve v_y= (2gd_y)^½

plug v_y into v_y= Rsinθ

solve for R

a_c=v_c²/r

F_c=ma_c or F_c=mv_c²/r

Y = A sin (ωt + Φ_o)

A = amplitude

ω = angular frequency

Φ_o = Initial phase

F_s = -kx

(horizontal displacement)

F_s=F_w

kx=mg

F_s=k(d+y) - mg

F = ma

F_parallel = F_wgt sinθ

F_normal = F_wgt cosθ

F_net = F_applied + F_friction + F_parallel

W = Fd

W = ΔPE and ΔKE and ΔE

p = mv

p_before = p_after

θ

degrees (°)

d

meters (m)

t

seconds (sec or s)

v

meters/seconds (m/s)

a

meters/second² (m/s²)

F

Newtons (N or kgm/s²)

f

Newtons (N)

μ

dimentionless (no unit)

wgt

Newton (N)

m

kilogram (Kg)

W

Joules (kgm²/s²)

E

Joules (J or Nm)

P

Watts (J/s)

g

9.8 m/s²

T

seconds/cycles (sec/cycle)

k

Newton/meter (N/m)

p

kilogram meter/second (kgm/s)

PE

Joules (J)

KE

Joules (J)

j

change in momentum (kgm/s)

Resultant vector

(SU)

Component vector

(SU)

Theta

(SU)

θ

unknown angle

Distance

(SU)

d

meters

m

Time

(SU)

t

seconds

sec or s

Velocity

(SU)

v

meter/seconds

m/s

Acceleration

(SU)

a

meters/second²

m/s²

Force

(SU)

F

Newtons

N or kgm/s²

Friction

(SU)

f

Newtons

N

Mu

(SU)

µ

dimensionless

no unit

Weight

(SU)

wgt

Newton

N

Mass

(SU)

m

kilogram

Kg

Work

(SU)

W

Joules

J or kgm²/s²

Energy

(SU)

E

Joules

J or Nm

Power

(SU)

P

watts

J/s

Gravity

(SU)

g

9.8 m/s²

Period

(SU)

T

seconds/cycles

sec/cycle

Spring constant

(SU)

k

newton/meter

N/m

Momentum

(SU)

p

kilogrammeter/second

kgm/s

Potential Energy

(SU)

PE

Joules

J

Kinetic Energy

(SU)

KE

Joules

J

Impulse

(SU)

Ft

change in momentum

kgm/s

Torque

(SU)

τ

Joule or Newtonmeter

J or Nm

Length of Torque arm

(SU)

l

meter

m

Amplitude of Spring

(SU)

x

meter

m

Gravitational Potential Energy

(SU)

U_G

Joules

J

Gravitational Force

(SU)

F_G

Newtons

N

force vs time graph

area under the line segment = Fxt 

 impulse = change in momentume