Understanding Motion: Distance, Displacement, Speed, Velocity, and Acceleration

1. Chapter 11 - Motion

2. How do you perceive motion? • Can two people look at the same object and only one of them see the object as moving? • One person says that your schools is 5 blocks from the library, and another says the 2 buildings are 7 blocks apart. Can both be right? • When you drop a rock off a cliff, how fast does the rock fall? • Can something that is slowing down also be accelerating? • We will take a look at these questions as we go through the chapter

3. 11.1 Distance and Displacement • To describe motion, you must state the direction and how fast the object is moving. • You must also tell is location at a certain time. • You also use a frame of reference if you want to describe it accurately. • Frame of reference – system of objects that are not moving with respect to one another • Tennis ball**

4. Frame of Reference • How fast are the train passengers in the picture moving? • If you are outside the train looking – they are moving quickly • If you are on the train with them – they don’t appear to be moving. • This is “frame of reference” • What we are describing is relative motion Relative motion – movement in relation to a frame of reference

5. Measuring Distance • Distance – lengthof a path between two points (measured in meters- the SI Unit) • It’s the actual path taken • Displacement – the direction from the starting pt. and the length of a straight line from the starting pt. to the ending pt. • The shortest distance between 2 points

6. Combining Displacements • Displacement is a vector. • Vector – a quantity that has magnitude and direction • Magnitude can be size, length or amount. • Arrowsused to represent vectors. • Length of arrow shows magnitude

7. Displacement along a straight line • When two displacements have the same direction, magnitudes are added. • If the two displacements are in opposite directions, magnitudes are subtracted. • What is the distance and displacement for A? B?

8. Displacement that’s NOT along a straight path… • When 2+ displacement vectors have different directions, they may be combined be graphing. • Notice the arrows (vectors) have arrows in the direction of movement and are placed tip to tail • Resultant vector – sum of two or more vectors (the red vector) • Which is the distance and which displacement? • If you take the length of the displacement vector, it equals 5 blocks while the distance walked is 7 blocks.

9. 11.2 Speed and Velocity • Speed – ratio of the distance an object moves to the amount of time it moves • Speed = distance/time (SI unit) • 2 ways to express speed of an object are: average speed and instantaneous speed • Average speed= total distance/total time v= • Instantaneous speed = measured at a particularinstant (like a speedometer) dt

10. Calculating Average Speed 1 • While traveling on vacation, you measure the times and distance traveled. You travel 35 kilometers in 0.4 hour, followed by 53 kilometers in 0.6 hour. What is your average speed? (v=d/t) • What info are you given? • Total Distance(d): • Total Time(t): • What are you trying to find? What formula do you need to find it? • Plug it in, Plug it in! • What’s the answer?

11. Calculating Average Speed 2 • A person jogs 4.0 kilometers in 32 minutes, then 2.0 kilometers in 22 minutes, and finally 1 km in 16 minutes. What is the jogger’s average speed in kilometers per minute?(v=d/t) • What info are you given? • Total Distance(d): • Total Time(t): • What are you trying to find? What formula do you need to find it? • Plug it in, Plug it in! • What’s the answer?

12. Calculating Average Speed 3 • A train travels 190 km in 3 hours, and then 120 kilometers in 2 hours. What is its average speed?(v=d/t) • What info are you given? • Total Distance(d): • Total Time(t): • What are you trying to find? What formula do you need to find it? • Plug it in, Plug it in! • What’s the answer?

13. Graphing Motion • Distance-time graph • Slope of a d-t graph shows speed • Slope is change in y (vertical) divided by change in x (horizontal) • Steeper line = faster speed • Straight line shows constant speed

14. Velocity • Velocity is speed in a given direction. • Velocity is a vector • Calculated the same way as speed. V=d/t • Velocities can be combined with vector addition V= 17 km/h The resultant velocity is 13 km/h

15. 11.3 Acceleration • We often think of acceleration when the speed of an object is increasing. However, acceleration results from increases OR decreases in speed. • Acceleration– the rate at which velocity changes • Can be change in speed OR direction • Acceleration is speeding up, slowing down, starting, stopping, or changing direction. • Acceleration is a vector. • Accel. = final velocity – initial velocity/time a = Vf –Vi / t

16. Free Fall t = 0 sv = 0 m/s t = 1 sv = 9.8 m/s • Free fall – movement of an object toward Earth because of gravity • Objects in free fall accelerate • Acceleration due to gravity near earth’s surface is a constant, g = 9.8 m/s2 • Imagine the stone in figure 12 falling from the mouth of the well. • After 1S the stone will be falling at 9.8m/s • After 2S the stone will be going faster by +9.8 to 19.6, then after 3 s, another 9.8 to 29.4 t = 2 sv = 19.6 m/s t = 3 sv = 29.4 m/s

17. Acceleration • Acceleration isn’t always the result of changes in speed. • You can accelerate even if your speed is constant • Riding a bike around a curve – you have a constantspeed, but your change in direction means you are accelerating • Sometimes you have change in speed and direction at the same time • A roller coaster ride starts out slowly as the cars travel up, they reach the top and plummet down. You are thrown around as your accelerationchangesconstantly.

18. Constant Acceleration • Constant Acceleration – steadychange in velocity • The velocity changes by the same amount each second • Ex: constant acceleration during takeoff results in changes in an aircraft’s velocity that are in a constant direction • You calculate acceleration for straight-line motion by dividing the change in velocity by the total time Acceleration = change in velocity = (Vf-Vi) totaltime t Do Math Skills on pg 346 1-4

19. Speed-Time Graphs Graphs of Accelerated Motion • Linear graphs display data • Speed-time graph • Slope shows acceleration • Straight line shows constant acceleration • Steeper slope shows greater increase or decrease per unit time

20. Speed vs. Time • Increase in speed is positiveacceleration.

21. Speed vs time • Decrease in speed is negative acceleration.

22. Distance-Time Graphs • A distance-time graph of accelerated motion is a curve • Increasingslope on a d-t graph means speed is increasing. • Instantaneous Acceleration – how fast velocity is changing at a specific instant Nonlinear graph

23. Can we answer the questions? • Can two people look at the same object and only one of them see the object as moving? • One person says that your schools is 5 blocks from the library, and another says the 2 buildings are 7 blocks apart. Can both be right? • When you drop a rock off a cliff, how fast does the rock fall? • Can something that is slowing down also be accelerating?