Linear Motion (8, 1)

Equations:

x = x0 + v0 ⋅

1

⋅ a ⋅ t

2

t + --

 

 

 

2

 

 

x = x0 +

1

⋅ (v0 + v) ⋅ t

--

 

2

 

 

 

1

⋅ a ⋅ t

2

x = x0 + v ⋅ t + --

 

2

 

 

v = v0 + a ⋅ t

Example:

Given: x0=0_m, x=100_m, t=10_s, v0=1_m/s

Solution: v=19_m/s, a=1.8_m/s^2.

Object in Free Fall (8, 2)

Equations:

1

⋅ g ⋅ t

2

y = y0 + v0 ⋅ t + --

 

2

 

 

v2 = v02 + 2 ⋅ g ⋅ (y + y0)

1

⋅ g ⋅ t

2

y = y0 + v ⋅ t + --

 

2

 

 

v = v0 + g ⋅ t

Example:

Given: y0=1000_ft, y=0_ft, v0=0_ft/s

Solution: t=7.8843_s, v= -253.6991_ft/s.

Projectile Motion (8, 3)

Equations:

 

 

 

 

 

1

 

2

x = x0 +v0 ⋅ COS(θ 0) ⋅ t

 

 

y = y0 + v0

⋅ SIN(θ 0) ⋅ t –

2--

⋅ g ⋅ t

 

vx = v0 ⋅ COS(θ 0)

 

 

vy = v0 ⋅ SIN(θ 0) – g ⋅ t

 

 

R =

v0

2

⋅ SIN(2 ⋅ θ 0)

 

 

 

 

--------

 

 

 

 

 

g

 

 

 

 

 

 

Example:

Given: x0=0_ft, y0=0_ft, Θ 0 =45_°, v0=200_ft/s, t=10_s.

Solution: R=1243.2399_ft, vx=141.4214_ft/s, vy= -180.3186_ft/s, x=1414.2136_ft, y= -194.4864_ft.

Equation Reference 5-35