1 D Motion motion in a straight line

1 -D Motion -- motion in a straight line

Introductory Concepts scalar vector magnitude, units, direction e. g. , mass (25 kg) weight (140 lbs. ) temperature (83 K) force (48 N )

distance (d) how far object travels -- depends on path taken Peoria displacement (Dx or Dy) the difference between the starting and ending points -- independent of path taken B-N displacement vector Memphis

For position coordinates x 1 and x 2, displacement is. . . Dx = x 2 – x 1 x 2 y 2 For position coordinates y 1 and y 2, displacement is. . . Dy = y 2 – y 1

speed (v) velocity (v) e. g. , 0. 12 m/s e. g. , 0. 023 m/s east x 1, t 1 x 3, t 3 x 2, t 2 d 2 Dx d 1

An Indy car takes 45. 7 s to go once around the 2. 50 -mile track at the Indy 500. Find the… a) …distance traveled. b) …displacement of the car. c) …average speed, in mph. d) …average velocity, in mph.

Graphical Analysis of 1 -D Motion Consider the following position-time curve. position (m) 15 10 5 0 0 slope of curve is: 1 2 3 4 5 6 7 time (s) Slope of a P-t curve at any time is object’s v at that time.

position (m) Find object’s velocity at t = 2. 0 s and at t = 6. 5 s. 15 10 5 0 0 1 2 3 4 5 6 7 (–) sign indicates that the object is moving opposite to how it started (which we assumed was the (+) direction). time (s)

instantaneous velocity: e. g. , police radar constant speed: e. g. , cruise control constant velocity: constant speed in a straight line

acceleration: “how quickly” velocity is changing -- speed up -- slow down -- change direction unit

Car traveling 65 m/s approaches stop sign. Driver applies brakes for 8. 2 s. Find car’s acceleration.

Car traveling 65 m/s slams into tree and stops in 0. 15 s Find car’s (and driver’s) acceleration.

Pygmy goat runs toward a feeding trough with initial velocity 2. 5 m/s. If goat slows down at 0. 42 m/s 2, how long will it take goat to reach trough?

An arrow is accelerated by a bowstring to 36 m/s in 0. 31 s. Find arrow’s acceleration.

Boy runs from inside garage and slides down icy driveway. At top, he moves at 2. 3 m/s. He slides down in 4. 5 s, accelerating at 0. 75 m/s 2. a Dt vi a. How fast is he moving at the bottom?

b. How long is the driveway? Dx Dt = 4. 5 s vi = 2. 3 m/s a = 0. 75 m/s 2 c. Assuming same acceleration, find the time for him to reach the bottom if he starts at the top from rest.

Penguin moves with initial speed 0. 65 m/s. At a later time, he has speed 1. 9 m/s. During this interval, penguin travels 7. 3 m. Find his acceleration. vi vf a=? Dx (derivation given on another slide)

Penguin moves with initial speed 0. 65 m/s. At a later time, he has speed 1. 9 m/s. During this interval, penguin travels 7. 3 m. Find his acceleration. vi = 0. 65 m/s, vf = 1. 9 m/s, Dx = 7. 3 m, a = ?

Linear Regression (Linear Least Squares Fit) a mathematical procedure that gives the “best” straight line through data points that don’t make a straight line . . . y=mx+b x

Using the Linear Regression Equation. . P. . v. . t slope = v . P. t slope = a . . . t 2

Consider a cat on a balance beam… P t An object is in free fall if the “only” force acting on it is gravity. a = g = – 9. 81 m/s 2 v 0 t a 0 t

Free Fall An alarm clock is “fire-escaped” from rest from height 38. 0 m a. How long is clock in the air?

b. Find velocity of clock at impact. c. Find velocity of clock halfway down.

A full beverage can is launched upward with initial velocity 22. 8 m/s. Find… a. …time to get to the top b. …total time in air

c. …maximum height attained (–) sign because g is and Dy is d. …location of can when its speed is half its original speed

Derivation 1 0 when vi = 0… So… ** NOTE: If vf = 0, we get…

Derivation 2 So…