Motion in one dimension

1. Motion in one dimension Test 2

2. Kinematics • - the branch of physics that describes motion in terms of x, v, a, and t • x- position (m) (sometimes d) • v- velocity (m/s) • a- acceleration (m/s²) • t- time (s) • Dynamics is kinematics + force exerted on an object.

3. Displacement • Defined as the change in position • f stands for final and i stands for initial • Units are meters (m) in SI • Example: If Xf = 30m and Xi = 20m what is the displacement?

4. Distance is different than Displacement • Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. • Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's overall change in position.

5. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. Distance traveled would be 2m +4m + 2m +4m = 12m Displacement would be 0m, you end where you started.

6. Displacement Xi =120m Xf = 5m ΔX= Xf - Xi ΔX= 5-120= -115 Negative displacement moves left or down; positive displacement moves right or up.

7. Displacement Examples • From A to B • xi = 30 m • xf = 52 m • x = 22 m • The displacement is positive, indicating the motion was in the positive x direction • From C to F • xi = 38 m • xf = -53 m • x = -91 m • The displacement is negative, indicating the motion was in the negative x direction

8. Position versus time graphs

9. Speed • The average speed of an object is defined as the total distance traveled divided by the total time elapsed (scalar quanity) • SI units are m/s (meters per second) • Always positive

10. Velocity • Velocity is magnitude and direction • 7 m/s East • If V is positive motion is to the right. • If V is negative motion is to the left. • Speed is the magnitude of velocity (no direction) • Velocity is a vector quanity

11. Velocity • It takes time for an object to undergo a displacement • The average velocity is the rate at which the displacement occurs • Velocity can be positive or negative • t is always positive

12. Speed vs. Velocity • Cars on both paths have the same average velocity since they had the same displacement in the same time interval • The car on the blue path will have a greater average speed since the distance it traveled is larger

13. Practice problem How fast is a train moving if it travels 25 m in 5 sec? Given: Solve: X=25m V = x/t V = 25m / 5 sec t=5s V = 5 km/s

14. Example Question • If a car travels 100 miles in 2 hours what is the velocity of the car? • ________ mph • Convert this is meters/second

15. A car travels 40 meters between the hours of 10am and 12am. What is the cars average velocity? Example question

16. A runner runs 3 seconds at 4m/s, stops for one second, and begins running for 2 seconds and covers 3m. • What is the velocity from (a) A to B, (b) B to C, and (c) A to D

17. Constant Velocity • Constant velocity is when an object’s velocity remains the same for a given amount of time. • An objects current velocity would be equal to the average velocity.

18. Acceleration • Changing velocity means an acceleration is present • Acceleration is the rate of change of the velocity • Units are m/s²

19. Which car has the greatest acceleration? Which line goes with which car?

20. Practice problem What is the acceleration of a car that travels from 20m/s to 50m/s in a period of 5s? Given: Solve: a = vf – vi t 20m/s = vi 50 m/s =vf a = 50m/s – 20m/s 5s 5s = t a = 6 m/s2

21. Velocity vs acceleration

22. We know that Vf= Vi + aΔt

23. You need to understand that.. • Xo = Xi • X= Xf

24. Motion in One Dimension with Constant Acceleration • V= Vo + at • X – Xo= ½ (v + vo)t • X – Xo= Vo t + ½ at2 • V2 - Vo2 = 2a (X – Xo)

25. Freely Falling Objects (3.3) An object moving under the influence of gravity alone. Regardless of its initial conditions.

26. Freely Falling objects • Drop something • Throw something and let it fall • Throw something down • Objects thrown upward or downward and those released from rest are all falling freely once released. • Once in freefall motion all objects experience the same acceleration; downward and equal to the acceleration due to gravity. (Earths Gravity= 9.8 m/s²

27. a= -g = 9.8 m/s² • V= Vo - gt • y – yo= ½ (v + vo)t • y – yo= Vo t - ½ gt2 • V2 - Vo2 = - 2g (y – yo)

29. Remarks… • Air resistance is neglected. All objects regardless of there mass will move at the same rate if they have the same initial conditions • Free fall motion is symetrical

30. JD drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. y-y. = v.t + 1/2gt2 -8.52m = 0 + .5(-9.8m/s2)t2 -8.52m = -4.9m/s2 t2 -8.52m/-4.9m/s2 = t2 1.7s2 =t2 1.3 s = t

31. Practice problem Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. V2 - Vo2 = - 2g (y – yo) Given: vi = 26.2 m/s vf = 0 m/s a = –9.8 m/s2 y = ?? (0 m/s)2 = (26.2 m/s)2 + 2(-9.8m/s2)y 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2)y 0 m2/s2 -686.44 m2/s2 =(-19.6 m/s2)y -686.44 m2/s2 =(-19.6 m/s2)y y = (-686.44 m2/s2)/ (-19.6 m/s2) y = 35.0 m

32. The observation deck of a skyscraper is 420 m above the street. Determine the time required for a penny to free-fall from the deck to the street below. y= -420m y-y.= v.t - ½ gt2 g =9.8m/s2 -420m = 0.5 (9.8m/s2)t2 -420m = -4.9m/s2t2 -420m/-4.9m/s2= t2 85.7m2/s2= t2 9.26s = t

33. Terminal Velocity • An object that falls will experience a force due to gravity and a force due to the air. • These forces are opposite in direction. • The object will reach a point where the forces balance, which means the object will no longer accelerate. It will continue with constant velocity. • Terminal velocity is the point reached by an object where it will no longer accelerate.

34. A Ball Thrown Up Consider a ball that is thrown straight up. • It will have maximum velocity the instant it leaves your hand and when it returns to your hand. (The ball is caught at the same height.) • On the way up, the ball will have negative acceleration, therefore the ball’s velocity will decrease.

35. Consider a rock thrown downward from a high altitude hot-air balloon. If the initial velocity is 15 m/s and air resistance is neglected, what is the acceleration of the rock after one second? What is the velocity of the rock? 9.8 m/s2