1. More More graphs of motion & Kinematic equations SEPTEMBER 11-14, 2015

2. Review: Slope of a P-T graph v = 10 m – 0 m 1s – 0 s = 10 m/s Once we know v, we can plot it on an V-T graph

3. Review: Slope of a P-T graph v = 10 m – 0 m 2s – 1 s = 10 m/s Once we know v, we can plot it on an V-T graph

4. Slope of a V-T graph a = 10 m/s – 0 m/s 1s – 0 s = 10 m/s 2 Once we know a, we can plot it on an A-T graph What do you think the slope of a V-T graph tells us? Acceleration!

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 Δx 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.. a)Which line has the highest acceleration? b)How do you know & how could you calculate that acceleration? c)Which line has the greatest displacement? c)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. 1)What is the acceleration between points C and D? 2)How far does the train travel between points A and C?

8. Kinematic Equations Let … t = the time for which the body accelerates a = acceleration v i = the velocity at time t = 0, the initial velocity v f = the velocity after time t, the final velocity x = the displacement covered in time t v f = v i + at v f 2 = v i 2 + 2ax

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: V i = 30m/s V f = 0 m/s t = 3.0 s What are we solving for: a Strategy: Use to solve for a. Solution: a = (v f – v i )/ t a = (0 m/s-30 m/s) / 3.0 s = -10 m/s 2 Evaluate answer: Yes! Units are correct, sign makes sense, and magnitude is reasonable. v f = v i + 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/s 2 ? 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/s 2 ? Sketch: Known variables: t = 10.0 s, v i = 2.00 m/s, a = 4.00 m/s 2 What are we solving for: x Strategy: Solution: 220 m Evaluate answer: Yes! Distance and sign make sense.

14. Acceleration Problems – You do 1) 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? 2) The car accelerate from rest to 28 m/s in 9.0 s. What distance does it travel? 3) A Jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s 2 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 1) 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/s 2 2) 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 2) A Jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s 2 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 v f 2 = v i 2 + 2ax