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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