Phys 250 Ch1 p1 Motion in One Dimension Mechanics:macroscopic objects Kinematics:describing motion Dynamics:studying the causes of motion Describing Motion Reference frame: Definition: [n] a system that uses coordinates to establish position Synonyms: coordinate system, frame of reference, reference system * often refers to a physical object Coordinate System: A system of assigning numbers to locate a point within a reference frame Consider a ball thrown straight up from the view point of the thrower from the view point of a passenger in a passing automobile *

Phys 250 Ch1 p2 Describing Motion Displacement: the change in the position of an object (includes sign, which indicates direction!)  x = x f – x i Example 2.2: You walk along a straight sidewalk for 45m, then turn around and walk 25 m in the opposite direction. You then walk 37 m in the original direction and stop. What is your displacement from your starting point? (hint: combine segments)

Phys 250 Ch1 p3 average speed: the ratio total distance s traveled to the time interval t required for the travel example: Fall Foliage Road Trip! Two students take a three hour trip to enjoy the fall foliage. In the first two hours they travel 100 km at a constant speed. In the third hour they travel another 80 km. What was their average speed for each hour of the trip? What was their average speed for the entire trip?

Phys 250 Ch1 p4 velocity: rate of change of displacement indicates speed and direction of travel average velocity: the ratio of the displacement during a time interval to the length if the time interval example: What is the average speed and average velocity of a helicopter if it takes of from the hospital and travels 150 km due east in one hour? if it takes of from the hospital and travels 150 km due west in one hour? if it takes of from a position 20 km east of the hospital and travels 50 km due east, then turns around and travels to a spot 80 km west of the hospital, all in one hour?

Phys 250 Ch1 p5 Graphical Interpretation of Velocity Velocity is the slope of the graph of position versus time may be positive or negative (direction!) steeper = faster math animation motion sensor exercise Instantaneous Velocity average velocity equals instantaneous velocity if velocity is constant displacement time tt xx

Phys 250 Ch1 p6 instantaneous velocity = slope of displacement versus-time graph displacement = area under the curve of velocity-time graph v t s = vt s t v t s = s 1 +s 2 = +v 1  t 1 +v 2  t 2 s t v1v1 t1t1 t2t2 v2v2 v t t1t1 t2t2  t3t3

Phys 250 Ch1 p7 acceleration: rate of change of velocity changes in speed as well as direction of travel average velocity: the ratio of the displacement during a time interval to the length if the time interval example: A bicyclist starts from rest and increases his velocity at a constant rate until he reaches a speed of 4.0 m/s in 5.0 s. What is his average acceleration?

Phys 250 Ch1 p8 Graphical Interpretation of acceleration Acceleration is the slope of the graph of velocity versus time may be positive or negative (direction!) Instantaneous Acceleration average acceleration equals instantaneous acceleration if acceleration is constant instantaneous acceleration = slope of velocity versus-time graph velocity = area under the curve of acceleration-time graph! velocity time tt vv

Phys 250 Ch1 p9 Motion with Constant Acceleration constant acceleration  slope of velocity-time graph is straight line displacement is area under velocity-time curve w/ substitution and some algebra The “Fab Four” v0v0 v = v 0 +at v t

Phys 250 Ch1 p10 Problem Solving Tips Draw a diagram Write down all known quantities, identify on diagram. Write down all unknown quantities, identify on diagram. Find basic equation which relates each unknown quantity to known quantities. Solve equation for the desired unknown. “plug and chug”

Phys 250 Ch1 p11 example: Suppose a child on a go-cart is traveling at 4.0 m/s when she crosses a line 4.0 m from her starting point. She then accelerates at a constant rate of 0.40m/s 2 until she crosses a line 40. m from the starting point. How long does it take her to go from the 4.0 m mark to the 40 m mark? example: A Boeing 777 airliner, initially at rest, undergoes a constant acceleration of 2.3 m/s2 down the runway for 34 s before it lifts off. How far down the runway does it travel? How fast is it going at lift off?

Phys 250 Ch1 p12 example: You are driving your new sports car at a speed of 90 km/h when you suddenly see a dog step into the road 50 m ahead. You hit the brakes hard to get the maximum deceleration of 7.5 m/s 2 (i.e. a = m/s 2 ). How far will you go before stopping?

Phys 250 Ch1 p13 Acceleration of Gravity Historical Perspective: Attempts to describe motion by Galileo Experiment and observation as the foundation of science ramps and freefall idealizations and simplifications: ignoring air resistance g = 9.81 m/s 2 (9.78 at equator, 9.83 at poles) = 32 ft/s 2 a = g, acceleration is directed downwards (watch directions in problems!!!)

Phys 250 Ch1 p14 example: On a Free Fall ride at an amusement park, riders are seated in a padded gondola and are taken to the top of a 10-story tower. The gondola is dropped 30 m down a vertical track (which curves at the bottom after which the gondola is slowed to a stop). How long does it take to fall the 30 m? What is the speed of the gondola at the bottom?