Motion

Motion a change in position, or location of a place or object, over a certain amount of time relies on a frame of reference or something assumed to be stationary is relative to a frame of reference i.e. – you may be stationary as you sit in your seat, but you are moving 30 km/sec (≈19 mi/sec) relative to the Sun Relative Motion Simulation

Speed the rate at which an object moves a measure of how fast something moves, or the distance it moves, in a given amount of time Formula: typically expressed in units of m/s is considered average when taking into account the total distance covered and the total time of travel is considered constant when it does not change is considered instantaneous when it represents a specific instant in time S = d t 00:00. 4 5 3 1 2 6 What is the ball’s speed? 6 meters

Interesting Speeds meters/second miles/hour Cockroach Kangaroo Cheetah 1.25 2.8 Kangaroo 15 34 Cheetah 27 60 Sound (in 200C air) 343 767 Space Shuttle (getting into orbit) 7,823 17,500 Light 300,000,000 671,080,888

Practice Problems - Speed If you walk for 1.5 hours and travel 7.5 km, what is your average speed? 2. Calculate the speed of a bee that flies 22 meters in 2 seconds. S = d t 7.5 km 5 km hr S = = 1.5 hr 22 m 11 m sec S = d t S = = 2 sec

The Speed Triangle S = d t t = d S d = S t . d d S t S . t

Distance-Time Graph Shows how speed relates to distance and time D 50 40 30 20 10 60 70 80 90 100 Time (seconds) 120 Distance (meters) D This distance-time graph will show a student’s speed as s/he returns to class after lunch. What is the speed from C-D ? What is the speed from B-C ? B C What is the student’s average speed? What is the speed from A-B ? A

Describe What’s Happening (distance-time graphs) Constant speed; away from starting point Constant speed; no movement Constant speed; toward the starting point

Can you figure this out? Two birds perched directly next to each other, leave the same tree at the same time. They both fly at 10 km/h for one hour, 15 km/h for 30 minutes, and 5 km/h for one hour. Why don’t they end up at the same destination?

Velocity the rate of change of an object’s position speed in a given direction is considered constant when speed and direction do not change changes as speed or direction changes is a vector can be combined Example If you are walking at a rate of 1.5 m/s up the aisle of an airplane that is traveling north at a rate of 246 m/s, your velocity would actually be 247.5 m/s north 10 m/s Does the ball have a constant velocity? What is the formula for calculating velocity? 29 m/s east 29 m/s west visuals taken from: http://www.amazing-animations.com/

Acceleration the rate at which velocity changes is a vector occurs when something is speeding up (+), slowing down (-), or changing direction Formula: typically expressed in units of m/s2 is always changing when traveling in a circle - centripetal 10 m/s Is the ball accelerating? a = vf – vi t Describe the car’s acceleration Describe the car’s acceleration a = 0 m/s – 10 m/s = -5 m/s2 2 s a = 50 m/s – 0 m/s = 10 m/s2 5 s

Understanding Acceleration Time (sec) Velocity (m/s) 1 2 3 4 5 When dropped, the ball will accelerate toward the center of the Earth at a rate of 9.8 m/s2 because of gravity. What will be the ball’s velocity at each second? 9.8 19.6 29.4 39.2 49.0

Practice Problems - Acceleration Tina starts riding her bike down a hill with a velocity of 2 m/s. After six seconds, her velocity is 14 m/s. What is Tina’s acceleration? 2. A motorcyclist goes from 35 m/s to 20 m/s in five seconds. What was his acceleration? a = vf – vi t 14 m/s - 2m/s 2 m s2 a = = 6 s a = vf – vi t a = 20 m/s - 35 m/s -3 m s2 = 5 s

Describe the student’s acceleration as she travels to class? Velocity-Time Graph Shows how acceleration relates to velocity and time 50 40 30 20 10 60 70 80 90 100 Time (seconds) 2 4 6 8 12 Velocity (meters/second) This velocity-time graph will show a student’s acceleration as she returns to class after lunch. Describe the student’s acceleration as she travels to class?

Describe What’s Happening (velocity-time graphs) Constant, positive velocity; away from starting point Constant, zero velocity Constant, negative velocity toward the starting point What do all of these velocity – time graphs have in common? How do these relate to the distance – time graphs? D T D T D T

Applying What You Have Learned Describe what’s happening in the graphs. How would it look on a distance-time graph? T D T D T

Momentum p = mv Formula: a measure of mass in motion is a vector the product of an object’s mass and velocity Formula: typically expressed in units of kg·m/s is in the same direction as the velocity makes an object harder to stop or change direction as it increases can be transferred is conserved p = mv 20 kg Which object has more momentum – the curling rock or the hockey puck? Explain your reasoning. Describe the scenario where the puck would have more momentum than the curling rock? 0.17 kg

Practice Problems - Momentum What is the momentum of a 7.3 kg bowling ball moving at 8.9 m/s? 2. At a velocity of 8.5 m/s, Tim moves down a hill on an inner tube. If his mass is 59 kg, how much momentum does he have? p = mv p = (7.3 kg) (8.9 m/s) = 65 kg·m/s p = (59 kg) (8.5 m/s) p = mv = 502 kg·m/s

Frame of Reference (Reference Point) a stationary location or object to which you compare other locations or objects none are truly stationary relative to all others – what is not moving in one is moving in another Task Using your body as the frame of reference, describe your classmate’s motion as s/he walks to the classroom door. How does your frame of reference impact your description compared to that of others? How does frame of reference explain why people thought the Earth was in the center of all celestial bodies?

Vector a quantity that has both direction and magnitude (size) drawn as an arrow which shows direction and magnitude (length of arrow) consists of two parts: tail and head Head Tail Consider the vectors above. Describe the direction and relative magnitude (speed) of each car based on the vector.

Combining Vectors can be combined/added What is the total velocity for each of the people/animals on the conveyor belt? 3 m/s 2 m/s 1 m/s 2 m/s 3 m/s dog belt 2 m/s belt ram 3 m/s man’s total velocity 2 m/s belt 1 m/s man 1 m/s dog’s total velocity ram’s total velocity = 0 m/s 2 m/s Image taken from: https://mholborn.sharepoint.com/sitepages/animated%20gifs.aspx