6 Acceleration Acceleration shows how fast velocity changes

6. Acceleration • Acceleration shows how fast velocity changes • Acceleration is the rate at which velocity is changing • Acceleration is the “velocity of velocity” 1

Example: The speed of a bicycle increases from 5 mi/h to 10 mi/h. In the same time the speed of a car increases from 50 mi/h to 55 mi/h. Compare their accelerations. Solution: We denote the time interval as Δt. Then the acceleration of the bicycle is: and the acceleration of the car is: Hence, the acceleration of the bicycle is equal to the acceleration of the car. 2

Question 1: If the velocity of a car is non-zero, can the acceleration of the car be zero? A) Yes B) No C) It depends Question 2: If the velocity of a car is zero, can the acceleration of the car be non-zero? A) Yes B) No C) It depends Question 3: The graph of position versus time for a car is given below. What can you say about the velocity of the car over time? x A) B) C) D) It speeds up all the time It slows down all the time It moves at constant velocity Sometimes it speeds up and sometimes it slows down E) Not really sure 3

7. Motion with constant acceleration - initial position - initial velocity Example: 4

8. Free fall acceleration: g=9. 8 m/s 2 Using the two base equations: Substitute the following into the base equations: To derive the following equations: 5

Example: A rocket is fired at a speed of 100 m/s straight up. (Neglect air resistance. ) a) How long does it take to go up to the highest point? b) What is the maximum height? c) How long does it take to return back (go up and fall back down)? d) What is the speed of the rocket just before it falls down? Given: Solution: a) At the highest point b) The maximum height is c) When it comes back d) The speed it falls down with is 6

9. Projectile Motion The trajectory of an object projected with an initial velocity at the angle above the horizontal with negligible air resistance. 7

Shoot the monkey (tranquilizer gun) A zookeeper shoots a tranquilizer dart to a monkey that hangs from a tree. He aims at the monkey and shoots a dart with an initial speed v 0. The monkey, startled by the gun, lets go immediately. Will the dart hit the monkey? A. Yes, as long as vo is large enough for the dart to reach the tree before it falls on the ground. B. No, it misses the monkey. If there is no gravity, the dart hits the monkey… If there is gravity, the dart also hits the monkey! 8

Continued If there is no gravity, the dart hits the monkey… 9

Continued If there is gravity, the dart also hits the monkey! Note, that it takes the same amount of time to hit the monkey as in the no gravity case! 10

Continued This might be easier to think about… For the bullet: For the monkey: 11