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Acceleration

Acceleration. Acceleration. Any change in velocity a = change in velocity/change in time a =  v/  t = m/s 2 Which car has the greatest acceleration?. Types of Acceleration.

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Acceleration

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  1. Acceleration

  2. Acceleration • Any change in velocity • a = change in velocity/change in time • a = v/ t = m/s2 • Which car has the greatest acceleration?

  3. Types of Acceleration • Example: A car is traveling at 1m/s when it reaches the edge of town. It then speeds up to 5 m/s in 20 seconds. What is its average acceleration? a = v/t a = 5m/s – 1m/s 20s =4m/s/20s = 0.20m/s2

  4. Graphing Acceleration • When an accelerating object’s motion is graphed on a position/time graph, the graph will be curved. • On a velocity/time graph, the slope of the line will be the objects acceleration. • To show acceleration, graph velocity on the y axis and time on the x-axis

  5. Types of Acceleration • Average • acceleration is over a length of time. • Instantaneous acceleration • Acceleration at an given instant in time.

  6. Constant Acceleration • Objects with constant acceleration • Vf = Vi + at • Example: If a car with a velocity of 2.0 m/s at t = 0 accelerates a rate of +4.0 m/s2 for 2.5s, what is its velocity at t = 2.5s? • Known? • Vi = 2.0m/s a = +4.0m/s2 t = 2.5s • Unknown= Vf • Vf = Vi + at • Vf = 2.0m/s + (4.0m/s2)(2.5s) • Vf = 12 m/s

  7. Acceleration Due to Gravity • Near Earth’s Surface, all objects fall toward the center of the Earth with an acceleration of • 9.80m/s2 • Ignoring air resistance. • Free Falls – objects fall with the acceleration due to gravity • Example: A ball is dropped from the roof and allowed to fall for 30s. What is the velocity of the ball when it hits the ground? • Vf = Vi + at • Vf­ = 0 + (9.80m/s2)(3 0m) • Vf = 294m/s

  8. Warm Up • If a ball is dropped off a cliff and lands with a velocity of 35m/s, how long was it falling?

  9. Warm Up • A penny is dropped off the Empire State Building, 381m tall. With what velocity will it hit the sidewalk?

  10. Constant Acceleration • Remember…. a = V/t • Using that formula, we can find many other pieces of information • During Constant Acceleration: • Velocity can be found by: • Vf = Vi + at

  11. Constant Acceleration • Displacement can be found if: • Time and Velocity are known • d = 0.5(Vf +Vi)t • Example: What is the displacement of a train as it is accelerated uniformly from +11m/s to +33m/s in a 20.0s interval? • d = 0.5(Vf + Vi)t • d = 0.5(33m/s + 11m/s)20.0s • d = +4.4 x 102m

  12. Checkpoint • How long does it take a car, starting from rest and accelerating at a rate of 2.5m/s2 to reach a velocity of 25m/s?

  13. Constant Acceleration (finding displacement • Acceleration and Time are Known • d = Vit + 0.5at2 • Because: • Vf = Vi + at and d = 0.5(Vf + Vi)t • We can sub the first equation for Vf in the second. • So, d = 0.5((Vi + at) +Vi)t • d = 0.5(2Vi + at)t • d = Vit + at2

  14. Constant Acceleration • Example: • A car starting from rest accelerates uniformly at +6.1m/s2 for 7.0 seconds. How far does the car move? • Given: Vi = 0 a = +6.1m/s2 t = 7.0s • d = Vit + 0.5at2 • d = (0)(7.0s) + 0.5(6.1m/s2)(7.0s)2 • d = 0 + 149.45m • d= 149.45m

  15. Constant Acceleration • Velocity and Acceleration are Known • Vf2 = Vi2 + 2ad • Because • Vf = Vi + at and d = 0.5(Vf + Vi)t • Solve first equation for t • t = (Vf - Vi)/a • Sub t into the second equation • d = 0.5(Vf + Vi)(Vf – Vi)/a • or d = (0.5(Vf – Vi)2 )/a

  16. Constant Acceleration • Example: An airplane must reach a velocity of 71m/s for takeoff. If the runway is 1.0km long, what must the constant acceleration be? • Given: Vi = 0m/s Vf = 71m/s d = +1.0km = +1.0 x 103m • Unknown: acceleration • Vf2 = Vi2 +2ad • 712m/s = 0.0m/s + 2(1.0 x 103)a • Solve for a • 712 m/s = 2(1.0 x 103)a • (712m/s)/((2)1000m) = a • a = 2.52m/s2

  17. Constant Acceleration • OVERALL, the four kinematics (motion for uniform acceleration) equations are: • Determine the variables you know and want to know • Determine the necessary equation

  18. A car is traveling at 55 m/s when it slows with an acceleration of -11 m/s2. How far does it take to stop? Known? Vi = 55m/s a = -11m/s2 Vf = 0m/s Unknown? D = ? Which equation? Vf2 = Vi2 + 2ad 02 = 552 + 2(-11)d 0 = 3025 + -22d -3025 -3025 -3025 = -22d -22 -22 137.5m = d Example

  19. If you drop a golf ball, how far does it fall in 0.5 s? Known? Vi = 0m/s t = 0.5s a = 9.8m/s2 Unknown? d = ? Which equation? d = Vit + 0.5at2 d = 0(d) + 0.5(9.8)0.52 d = 0 + 4.9(0.25) d = 1.225m Example 2

  20. A steam driven catapult accelerates a 20 ton aircraft from 0 to 66 m/s in 3.0 s to launch the plane from the deck of an aircraft carrier. Find the rate of acceleration. Known? Vi = 0 Vf = 66m/s T = 3.0s Unknown? a = ? Which equation? Vf = Vi + at 66 = 0 + a(3.0) 3.0 3.0 22m/s2 = a Example 3

  21. Warm Up • A penny is dropped off the Empire State Building, 350m high. How fast is it going when it hits the ground?

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