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9/4 Acceleration

9/4 Acceleration. Text sections 2.1-3 and 1.5-6 HW “9/4 Airplane” due Friday 9/6 On web or in 213 Witmer for copying For Thursday, look at text sections 2.7 and 3.1-2 Graphing and 2-D Motion Suggested Problems: 2-25, 26, 29, 30. v f =. v i =. v = 4m/s left. v ave = 2m/s down the ramp.

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9/4 Acceleration

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  1. 9/4 Acceleration • Text sections 2.1-3 and 1.5-6 • HW “9/4 Airplane” due Friday 9/6 On web or in 213 Witmer for copying • For Thursday, look at text sections 2.7 and 3.1-2 Graphing and 2-D Motion • Suggested Problems: 2-25, 26, 29, 30

  2. vf = vi = v = 4m/s left vave = 2m/s down the ramp Example Problem A block slides from rest down a ramp, across a level section, then down another ramp of equal slope. Ignore friction. On the lever section the block moves with a constant velocity of 4m/s. 0m/s 4m/s What is the block’s average velocity on the upper ramp? The average of 0 and 4 is 2.

  3. Average Velocity Average velocity is the “middle” velocity as well as x/t. • Example: • An object slows down from 35m/s to 5m/s, what is the average velocity? • It took 6s to slow down, how far did the object move? • What is its speed at 3s, the “mid-time?”

  4. v a = t a points down the ramp. Turnaround point Draw v, (from i to f) which points the same direction as a. vf vi vi vf v Acceleration • A ball rolls up and down a ramp as shown in the strobe photograph. Which way does the acceleration point or does the acceleration = 0? Pick a time interval, ti - tf and draw velocity vectors Draw velocity vectors tail to tail Ball rolling up the ramp tf ti

  5. Acceleration and Velocity • Example: • An object moving left slows down from 35m/s to 5m/s, what is the average velocity direction? • It took 6s to slow down, what is the object’s acceleration, magnitude and direction? (Always think about v.) v = 30m/s to the right a = 5m/s2 to the right

  6. Turnaround point Acceleration at turnaround • A ball rolls up and down a ramp as shown in the strobe photograph. At the turnaround point, which way does the acceleration point or does the acceleration = 0 there?

  7. Turnaround point Turnaround point Draw v, (from i to f) which points the same direction as a. vf v vi vf vi v Acceleration at turnaround Even though v = 0, v is still changing and there is acceleration!!!! Pick a time interval, ti - tf and draw velocity vectors Copy velocity vectors tail to tail ti Ball rolling up the ramp Ball rolling down the ramp tf

  8. is an “operational definition” in that it defines a procedure for finding and using a. v a = t Acceleration Finding acceleration Using Acceleration

  9. v = 8m/s v = -4m/s left v = 4m/s v = -4m/s left v = 0m/s v = -4m/s left v = -4m/s v = -4m/s left v = -8m/s v = -4m/s left v = -12m/s “Change in Velocity” Vector, v Even though the object slows down, turns around, and speeds up in the opposite direction; v is constant! The “change in velocity” vector may point with or against the velocity vector.

  10. v Acceleration is a vector that points in the same direction as the “change in velocity” vector. In this case, a = 4m/s/s left. a = t v = 8m/s v = -4m/s left v = 4m/s v = -4m/s left v = 0m/s v and a point opposite,slowing down v = -4m/s left v = -4m/s v = -4m/s left v = -8m/s v = -4m/s left v = -12m/s v and a point the same direction,speeding up Acceleration In concept, it is “the amount and direction the velocity changes each second.”

  11. Displacement, x (distance moved) Average Velocity, vave (average over time) Instantaneous Velocity, v (at a particular time) Change in Velocity, v (speeding up or slowing down) Acceleration, a (how much the velocity changes each second) Concepts so far-

  12. Problem: An object goes from a velocity of 15 m/s right to 6 m/s right in 3 seconds. Find the acceleration, both its size (magnitude) and its direction, (left or right). How do the directions of the velocity and acceleration compare? What is the object doing during these 3 seconds? How far did the object travel during these three seconds? Hint: What is the average velocity? What will the objects velocity be in three more seconds if the acceleration stays the same?

  13. Problem: A bullet exits a rifle at 85m/s. The barrel is 0.75m long. What is the acceleration of the bullet? Don’t use text equations, just the relationships between displacement, time, velocity and acceleration

  14. 30 v = = 5m/s/s right a = 6 t vi = 10m/s v = 30m/s right vf = 40m/s Finding acceleration t = 6s Return

  15. v = 10 m/s north vave = 7 m/s north x = 14 m north Problem: • A bear is running 4 m/s north. The acceleration of the bear is 3m/s2 north. What is the bear’s velocity 2 seconds later? • What is the bear’s average velocity? How far did the bear run during this time? Return

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