Unit 5

This unit was a culmination of information we have learned from previous units, but this time we included horizontal vs. vertical directions. 
Horizontal equations
v=∆x/∆t
xf=vt+xi
models: CVPM, BFM
horizontal velocity=vx

Vertical equations
a=∆v/∆t
∆x=1/2at^2+vit
vf=at+vi
models: CAPM, UFPM
vertical velocity=vy

Meta Sheet

• If an object is moving downwards, the velocity and acceleration will be negative
• key words: upwards= positive and downwards=negative
• acceleration at the top of vertical= -10m/s^2 and velocity at top= 0m/s
• acceleration at the top of horizontal=0m/s^2 and velocity at top=constant
• for two dimensional maps, x-axis is always straight
• if problem gives you vi at an angle, you cannot use it for vertical & horizontal
• do NOT plug horizontal distances into vertical problem equations 
• remember in the quadratic equation: take square root and then solve +/- part

Example Problems 

A gum ball is thrown downward with an initial speed of 20m/s. Find the displacement of the gum ball after 4 seconds. Next, find the time it takes to reach a velocity of 50m/s and how long it would take to fall 100m.
Vertical
viy=-20m/s (because it's falling down)**
a=-10m/s^2

Displacement
∆x=1/2at^2+vit
∆x=1/2(-10)(4)^2+(-20)(4)
∆x=-80-80
∆x=160m

Time it takes to reach a velocity of -50m/s
vf=at+vi
-50=(-10)t+(-20)
-30=-10t
t=3s
**remember to change Vi, Vf, and a to negative if it's falling down or else you will get a completely different answer**

Time it takes to fall 100m **Negative 100m because it's falling**
∆x=1/2at^2+vit
-100=1/2(-10)t^2+(-20)t
0=-5t^2+(-20)t +100
-5=a -20=b 100=c
Quadratic equation time!