1. Acceleration and Deceleration Section 7.4

2. Acceleration Acceleration is the rate of change of the rate of change. In other words, acceleration = f’’(x) = second derivative of the function *If f’’(x) is negative, the object is… decelerating!

3. Example 1 Find the instantaneous vertical acceleration at time t of a projectile whose height at time t is given by h(t) = 4 + 55t - 16 t 2. h’(t) = 55 – 32t feet per second h’’(t) = -32 feet per second per second

4. Example 2 A ball is dropped from the Leaning Tower of Pisa, 56 m above the ground. The height (in meters) of the ball above the ground at time t seconds is given by h(t) = –4.9t 2 + 56. a. What is the instantaneous velocity of the ball at time t = 3 sec.? b. What is the acceleration of the ball at time t = 3 seconds? c. At what time t does the ball hit the ground? d. What is the instantaneous velocity of the ball at the moment it hits the ground? h’(t) = -9.8th’(3) = -9.8(3)h’(3) = -29.4 m/second h’’(t) = -9.8 h’’(3) = -9.8h’’(3) = -9.8 m/sec / sec 0= -4.9t 2 + 56-56= -4.9t 2 11.43= t 2 T = 3.38 sec h’(3.38) = -9.8(3.38) h’(3.38) = -33.13 m/sec

5. Homework Pages 442 – 443 4 – 6, 8 – 9, 12