Chapter 11: Motion

11.1 – Distance & Displacement

Describing Motion In this chapter, we will be studying and describing motion.  Motion = a change in position in an amount of time

Frame of Reference  To describe motion accurately, a frame of reference is necessary!  Frame of Reference- a system of objects that are NOT moving with respect to one another. OR… The background that you are using to judge motion.   

What would be a good frame of reference to use when describing the car’s motion?

Answer: The tree

The motion of an object looks different to observers in different frames of reference. Ex: Astronauts in space vs people on Earth Apollo-13 quote : They’re back inside, looking up at us”

It’s All Relative  Since the description of the motion depends on the frame of reference, there can be several correct answers to describe the motion …depending on which frame of reference you use.

Example: Is the person in the car moving?

Yes, relative to the tree No, relative to the car  In other words, it’s all relative!  Relative Motion- movement in relation to a frame of reference

MEASURING DISTANCE AND DISPLACEMENT http://www. youtube. com/watch

DISTANCE & DISPLACEMENT To describe an object’s position, you need to know its distance and direction from a certain point. Distance- the length of a path between 2 (two) points What is the SI unit for distance? METER

Example: length of the Pere Marquette trail

Displacement: the direction from the starting point and the length of a straight line from start to end. (how far gone from the original position)   

Compare the distance Compare the displacements

If you travel in a circle…

…you will end up with a displacement of zero!

Vectors

Vectors http://www. youtube. com/watch. v=fVq4_HhBK8Y http://www Vector = a quantity that has magnitude and direction Magnitude refers to size, length, or amount Arrows represent vectors The length of the arrow represents magnitude The arrow points in a direction

Displacement is an example of a vector.  Displacement = length of path + direction

Vector Addition You can add up (combine) displacements using vector addition  When two displacements are in the same direction, add the magnitude of their vector arrows. When they are in opposite directions, subtract their magnitudes from each other. 

Examples of Vector Addition in the same direction

Examples of Vector Addition in different directions

Vector Addition If the path is not straight, all the vectors can be “added” combined together for a total.  To get the total displacement (start to finish), use a resultant vector.

Resultant Vector How would its magnitude be calculated? a2 + b2 = c2

11. 2 Speed and Velocity http://www. youtube. com/watch  

SPEED Speed = Distance  Time Speed: The ratio of the distance an object moves to the amount of time the object moves The SI unit for speed is m/s Meters for distance Seconds for time However, be sure to choose a suitable SI (prefix such as kilo-)unit to measure speed

Calculating Speed This will be a “quick and easy” way to help you solve for ANY three of the variables in the formula for speed! Speed Triangle: D S T

Speed Triangle

Sample problems 1) A student practicing for a track meet ran 250m in 30s. Calculate her speed.

1) Speed = 250m/30s = 8.3m/s

2) If an object’s speed is 5m/s how long will it take to go 300m?

2) Time = 300m/5m/s = 60s

3) How far will a plane go if it travels for 3hrs at a speed of 400km/hr?

3) Distance = 400km/hr x 3hrs = 1200km

Types of Speed Two ways to express speed are average speed and instantaneous speed Average speed is calculated for the entire duration of a trip The speed may vary during the trip, but the following equation will tell the average speed over the entire trip

Calculating Speed Average Speed = total distance/total time Example: A car travels 60km in 2hrs and then 100km in 3hrs. Calculate average speed!

Average Speed = 60km + 100km 160 km ------------------- = ---------- = 2hr + 3hr 5 hr 32km/hr

Instantaneous Speed Instantaneous speed is measured at a particular instant Example: Measured on the speedometer

Graphs of Motion Graphing Motion In this chapter we will use graphs to help us analyze motion. A distance-time graph is a good way to describe motion

Graph of Speed A Distance-Time Graph

Slopes on a Distance-Time Graph What does the slope of the line represent? The slope of a line on a distance-time graph is speed!!! Slope = change in y  change in x = rise  run =SPEED!!!

Slopes on a Distance-Time Graph Question: What does a steeper slope on a distance-time graph represent? Answer: A higher speed

Velocity Knowing just the speed of an object is not always enough information to accurately describe its motion You need to know speed AND direction of the object’s motion

Velocity: the speed and direction in which an object is moving To calculate velocity: V = D/T + DIRECTION

Velocity & Vectors Velocity is a vector Velocity = speed + direction Longer vectors represent faster speeds Shorter vectors represent slower speeds The direction of the vector arrow represents the object’s direction Velocity can change as a result of a change in speed, direction, or both

Question: When would an object’s motion involve more than one velocity?

Answer: For example, when a boat is traveling downstream It has its own velocity, Vb Plus the velocity of the current of the river,Vr

More than one velocity

Velocity & Vector Addition When there are 2 or more velocities add by vector addition *Remember: If the vectors are in the same direction, add them. Opposite directions, subtract. Right triangle use P. T.

11-3 Acceleration

Some Review Question: What is velocity? Answer: A combination of speed and direction So to determine the rate at which velocity changes we use acceleration

Acceleration Acceleration- the rate at which velocity changes (over time) What would the units for acceleration be?

Velocity units are m/s then divide by time (s) Acceleration Unit = m/s2 or m/s/s

Is it a Vector??? Question: Is acceleration a vector?

Is it a Vector??? Answer: YES If velocity is a vector and acceleration is a change in velocity, than acceleration is a vector, too!

Acceleration Acceleration can be described as Changes in speed, Changes in direction, Or changes in both

Acceleration So, a change in speed, or direction, or BOTH can cause acceleration!

Classifying Acceleration Speeding up = (+) positive acceleration Slowing down = (-) negative acceleration or deceleration

Free Fall Example of acceleration due to change in speed: FREE FALL- the movement of an object toward Earth solely because of gravity The rate of acceleration downward toward the Earth during free fall is 9.8 m/s2

FREE FALL

Free Fall as object falls, or free falls toward the Earth, each second its velocity increases downward by 9.8 m/s

Question: What would velocity be of an object in freefall after 2s?

Answer: 9.8m/s/s x 2s = 19.6m/s

Changes in Acceleration Question: When could you have acceleration due to a change in direction?

Example: The carousel

Changes in Acceleration While the speed is remaining constant, the horses on the carousel are constantly changing their direction

Changes in Acceleration What about changes in speed and direction at the same time?!?! Question: When would you see acceleration due to both (changes in speed and direction)?

   Roller Coaster!!!

Constant Acceleration Constant acceleration- a steady change in velocity. The velocity of the object is changing by the same amount each second. Example: Freefall at 9.8 m/s/s

CALCULATING ACCELERATION You can calculate acceleration for straight-line motion by dividing the change in velocity by the total time. 

Parts of the Formula a = ACCELERATION vf = FINAL VELOCITY vi = INITIAL VELOCITY t = TOTAL TIME Acceleration = Change in Velocity = (vf – vi)                                   Total time t

Positive Acceleration Using the formula, you can see that an increase in velocity will result in a positive change in velocity (because vf is larger than vi) Positive change in velocity = a positive acceleration.

Calculate: What is the acceleration of a runner who begins running at a speed of 5m/s and after 6s is running at 10m/s.

Answer: 10m/s – 5m/s = 0.83 m/s/s or m/s2

Calculate acceleration: a car at a stop sign accelerates to 12m/s in 6s.

12m/s – 0m/s 6s Answer: 2m/s/s OR 2 m/s2

Negative Acceleration (a.k.a. Deceleration) If the velocity decreases, however, from start to finish, than the numerator in the equation will be negative and so will the acceleration (because Vi will be greater than Vf)

Calculate acceleration: a runner who was running at 6km/hr suddenly trips and falls coming to a complete stop in 8s.

0km/hr – 6km/hr 8s Answer: -0.75km/hr/s

Calculate the acceleration of a car that is traveling at a speed of 80 km/h that slows to 60 km/h in 4 s when the driver spots a police officer.

60 km/h – 80 km/h = - 5 km/h/s 4 s

GRAPHS OF ACCELERATED MOTION using velocity(speed)-time graphs

Review: Question: What is the slope of a distance-time graph?

Answer: change in distance/change in time = speed!

Q: What would be the slope of a speed-time graph Q: What would be the slope of a speed-time graph? (Hint: the slope is change in speed divided by change in time.)

A: Acceleration!!!

Question: When looking at a speed-time graph, what does a straight line sloping upward represent?

Answer: Constant positive acceleration

Question: What does a negative slope usually tell us about the motion of the object?

A: It is decelerating, or slowing down.

Remember…Acceleration on a Distance-Time Graph Data for an object plotted on a distance-time graph would create a nonlinear graph (curve)