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LINEAR MOTION

LINEAR MOTION. Chapter 2. Motion . Everywhere – people, cars, stars, cells, electricity, electrons Rate = Quantity/time How fast something happens. Linear Motion. Motion on a straight path Scalar- Distance and speed Vector – Displacement and velocity. Motion is Relative.

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LINEAR MOTION

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  1. LINEAR MOTION Chapter 2

  2. Motion • Everywhere – people, cars, stars, cells, electricity, electrons • Rate = Quantity/time • How fast something happens

  3. Linear Motion • Motion on a straight path • Scalar- Distance and speed • Vector – Displacement and velocity

  4. Motion is Relative • Everything moves • Things that seem at rest are moving in relation to stars and sun • Book on a desk moves at 30 km/sec in relation to the sun • Same book is even faster in the galaxy • In this chapter – we look at motion compared to earth

  5. Speeds • Snail - 2 meters/day • Indy racecar – 300 km/hr • Space shuttle – 8 km/sec

  6. Speed • Distance / time • “per” – divided by – “/” • Any combination of units is useful depending on situation • Km/hr, cm/day, light-years/hour • Most common – m/sec and mile/hr

  7. Average Speed • Total distance/time interval • Examples: • 60 km in 1 hour = 60 km/hr • 240 km in 4 hour = 60 km/hr • Note the units • Does not indicate all the stops and starts

  8. The longer the time period measured, the more it leads to calculating an average velocity.

  9. Constant Speed • If the speed does not change over a long period, it is like Average speed • Length = velocity x time • l = vcont

  10. Instantaneous Speed • Speed at any moment • Speed can vary with time • Speedometer – measures instantaneous speed

  11. Chapter Chapter Assessment Questions 2 Question 2 Refer the adjoining figure and calculate the distance between the two signals? • Insert graph • 3 m • 8 m • 5 m • 5 cm

  12. Chapter 2 Chapter Assessment Questions Answer 2 Answer:C Reason:Distance d = df – di Here, df = 8 m and di = 3 m Therefore, d = 8 m  3 m = 5 m

  13. Questions • The speedometer in every car also has an odometer that records distance: • If the odometer reads zero at the beginning of the trip and 35 km a half-hour later, what is the average speed? • Would it be possible to attain this average speed and never exceed 70 km/hr? • If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In one minute?

  14. Graph of Constant speed • Average speed is the slope of the line during an interval • If it is a curve, the instantaneous speed is the line tangent to the curve at that point

  15. Delta Notation • Δ – Greek capital letter – Delta • Signifies a change in a quantity Δl = l f – l i Δt = t f -t i v = Δl = l f – l i Δt t f - t i

  16. Velocity • EDL (every day life) – speed and velocity are interchangeable • Physics – Velocity – speed in a direction • 60 km/hr North • Question – The speedometer of a car moving northward reads 60 km/hr. It passes another car that travels southward at 60 km/h. Do both cars have the same speed? Do they have the same velocity?

  17. Constant Velocity • Constant speed and direction • Must move in a straight line • Curves change the direction • Changing velocity- in a car there are 3 things to change velocity – • Gas • Brakes • Steering wheel

  18. The Displacement Vector • Displacement is the straight-line shift in position from Poto Pf • Included length and direction • Vector • Magnitude • Direction

  19. Resultant • The vector that is drawn between two points Resultant

  20. Vector Algebra • Rules for dealing with vectors • Helps us understand how to manipulate them

  21. Tip-to-Tail Method • Add vectors by placing tip of one to the tail of the other. • The resultant is from the tail of one to the tip of another A B B A Resultant

  22. Tip-to-Tail Method • Order of addition is irrelevant B A A B B A

  23. Parallelogram Method • Use 2 set vectors to make a parallelogram • The diagonal is the resultant

  24. Multiple Vectors • Add more than 2 vectors by the tip-to-tail method Resultant Resultant

  25. Parallel Vectors • Parallel – Simple sum • Anti-parallel (opposite directions) - Difference Resultant Resultant

  26. Acceleration • How fast is velocity changing • Acceleration is a RATE (of a rate) • Change in velocity • Acceleration • Deceleration • Change in direction • Acceleration = Change in velocity/time

  27. Question • Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then 45 to 50 km/h. What is its acceleration? • In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. Which undergoes greater acceleration? What is the acceleration of each vehicle?

  28. Average Acceleration a – acceleration (m/s^2) v – velocity (m/s) t – time (s)

  29. Average acceleration problem Problem – What is the acceleration of a car the screeches to a stop from 96.54 km/h in 3.7 seconds?

  30. Instantaneous Acceleration • Velocity vs. Time graph • Slope of line tangent is equal to ACCELERATION • Sign of Slope • Positive – accelerating • Negative - decelerating

  31. Velocity-Time Graph of Accelerating Car Tangent Slope = acceleration velocity time

  32. Uniform accelerated motion • In the real world, acceleration is seldom constant • In problems, we can consider it constant for a few moments • Motion is in a straight line • Vf – final velocity • Vi – initial velocity

  33. Uniform accelerated motion • vf = vi + at • Problem – What is the final speed of a bicyclist moving at 25.0 km/h who accelerates +3.00 m/s^2 for 3.00 sec?

  34. The Mean Speed • What is vav for an object that is uniformly accelerating from vi to vf? Mean speed = vav = ½ (vi + vf)

  35. Area under the Graph • Equals the total distance moved Area of a retangle = m/s x s = Meters

  36. More complex • Area under still equals distance

  37. Mean Speed Theorem s = ½ (vi + vf) t Problem- A bullet is fired with a muzzle speed of 330m/s down a 15.2 cm barrel. How long does it take to travel down the barrel?

  38. Constant Acceleration Equations THE BIG FIVE • vf = vi + at • vav = ½ (vi + vf) • s = ½ (vi + vf) t • s = vit + ½ at² • vf² = vi² + 2as

  39. When vf is unknown • One sports car can travel 100.0 ft in 3.30 seconds from 0m/s. What is the acceleration?

  40. When t is unknown Problem – What is the cheetah’s acceleration if it goes 0 to 72 km/hr in 2.0 seconds? - How far will it go to be moving 17.9 m/s?

  41. Freefall – How Fast • An apple gains speed as it falls • Gravity causes acceleration • EDL – air resistance effects freefall acceleration

  42. Freefall Elapsed Time Instant. Speed (m/sec) 0 0 1 10 2 20 3 30 4 40 t 10t

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