Calculus 12
Name:
Lesson 6.1 DISTANCE, VELOCITY, AND ACCELERATION
APPLICATIONS OF DERIVATIVES
DISPLACEMENT (s)
𝑑𝑠
VELOCITY (𝑣 = 𝑑𝑡)
ACCELERATION (𝑎 =
distance and direction from initial position (0)
𝑠 > 0 positioned right or up
𝑠 < 0 positioned left or down
𝑠 = 0 origin
change is displacement with respect to time
𝑣 > 0 moving right or up
𝑣 < 0 moving left or down
𝑣 = 0 stationary
𝑑𝑣
𝑑𝑡
𝑑2 𝑠
= 𝑑𝑡 2 )
speed =|𝑣|
increasing or decreasing in speed
𝑎 > 0 accelerating
𝑎 < 0 decelerating
𝑎 = 0 constant velocity
Example 1 p. 262
Example 2 p. 265
GENERAL EQUATION: for particles moving due to gravity
1
𝑠 = 𝑎𝑡 2 + 𝑣𝑡 + ℎ
2
CYDI for
1
𝑠 = 2 𝑎𝑡 2 + 𝑣𝑡 + ℎ
Do page 267 #1,2,3
earth’s gravity is -9.8m/s
a) find velocity function
b) find acceleration function