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More graphs of motion & Kinematic equations

More graphs of motion & Kinematic equations. September 11-14 , 2015. Review: Slope of a P-T graph. We can calculate the average velocity from a P-T graph by finding the slope of the graph. Remember: v avg = = = slope of P-T graph. 10 m – 0 m. v =. = 10 m/s. 1s – 0 s.

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More graphs of motion & Kinematic equations

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  1. Moregraphs of motion & Kinematic equations September 11-14, 2015

  2. Review: Slope of a P-T graph We can calculate the average velocity from a P-T graph by finding the slope of the graph. Remember: vavg = = = slope of P-T graph 10 m – 0 m v = = 10 m/s 1s – 0 s Once we know v, we can plot it on an V-T graph

  3. Review: Slope of a P-T graph What if it’s a curvy line? We can still just pick two points on the graph and use the formula: vavg = = 10 m – 0 m v = = 10 m/s 2s – 1 s Once we know v, we can plot it on an V-T graph

  4. What do you think the slope of a V-T graph tells us? Acceleration! Slope of a V-T graph We can calculate the acceleration from a V-T graph by finding the slope of the graph. Remember: a = = = slope of V-T graph 10 m/s – 0 m/s a = = 10 m/s2 1s – 0 s Once we know a, we can plot it on an A-T graph

  5. Area under Motion graphs Another important thing to know is that the area under the curve in a motion graph has meaning. area under V-T graph = Δx Δx = area under V-T graph How do you find the area of a triangle? Area = ½ base * height Δx = ½ * 5 s * 50 m/s = 125 m Area = Δx

  6. Test your understanding Think about your answer, wait until I tell you, then show me the answer by holding up the correct number of fingers. . Which line has the highest acceleration? How do you know & how could you calculate that acceleration? Which line has the greatest displacement? How do you know & how could you calculate that displacement? 1 # 1 has the steepest slope. We could calculate a by finding the slope. # 2 has the greatest displacement. # 2 has the largest area under the line. We could calculate displacement by finding that area.

  7. You do Use the graph of the motion of a toy train, below, to answer the questions. What is the acceleration between points C and D? How far does the train travel between points A and C?

  8. Kinematic Equations Up until now, we’ve had just two kinematic equations: vavg= and a = These can be re-written in to more user-friendly forms … Let … t = the time for which the body accelerates a = acceleration vi= the velocity at time t = 0, the initial velocity vf= the velocity after time t, the final velocity x = the displacement covered in time t = x = vi t + 2 vf2 = vi2 + 2ax vf = vi + at

  9. Problem Solving Strategy • Diagram the problem • List known variables • Determine what you are trying to find. • Determine your strategy • Solve the problem • Evaluate your answer. Check whether the units, sign, and magnitude make sense.

  10. Acceleration Problems – We do Grace is driving her sports car at 30 m/s when a ball rolls out into the street in front of her. Grace slams on the brakes and comes to a stop in 3.0 s. What was the acceleration of Grace’s car? Sketch: Known variables: What are we solving for: Strategy: Solution: Evaluate answer:

  11. Acceleration Problems – We do Grace is driving her sports car at 30 m/s when a ball rolls out into the street in front of her. Grace slams on the brakes and comes to a stop in 3.0 s. What was the acceleration of Grace’s car? Sketch: Known variables: Vi = 30m/s Vf = 0 m/s t = 3.0 s What are we solving for: a Strategy: Use to solve for a. Solution: a = (vf – vi)/ t a = (0 m/s-30 m/s) / 3.0 s = -10 m/s2 Evaluate answer: Yes! Units are correct, sign makes sense, and magnitude is reasonable. vf = vi + at

  12. Acceleration Problems – We do What is the displacement after 10.0 s of a mass whose initial velocity is 2.00 m/s and moves with acceleration a = 4.00 m/s2 ? Sketch: Known variables: What are we solving for: Strategy: Solution: Evaluate answer:

  13. Acceleration Problems – We do What is the displacement after 10.0 s of a mass whose initial velocity is 2.00 m/s and moves with acceleration a = 4.00 m/s2 ? Sketch: Known variables: t = 10.0 s, vi = 2.00 m/s, a = 4.00 m/s2 What are we solving for: x Strategy: Solution: 220 m Evaluate answer: Yes! Distance and sign make sense. x = vi t + 2

  14. Acceleration Problems – You do • A car has an initial velocity of 5.0 m/s . When its displacement increases by 20.0 m, its velocity becomes 7.0 m/s. What is the acceleration? • The car accelerate from rest to 28 m/s in 9.0 s. What distance does it travel? • A Jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s2 as it comes to a rest. Can this plane land at an airport where the runway is 0.80 km long?

  15. Acceleration Problems – You do • A car has an initial velocity of 5.0 m/s . When its displacement increases by 20.0 m, its velocity becomes 7.0 m/s. What is the acceleration? Strategy – use Answer: 0.6 m/s2 • The car accelerates from rest to 28 m/s in 9.0 s. What distance does it travel? Strategy, find a then find x. Answer: 126 m • A Jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s2 as it comes to a rest. Can this plane land at an airport where the runway is 0.80 km long? Use Answer: No – it needs 1000 m vf2 = vi2 + 2ax vf2 = vi2 + 2ax

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