9/4/2017. Motion: Acceleration

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Motion Position, velocity Acceleration Reminders: HW 1 due tonight, 1pm on D2L Homework 2 available on D2L Reading quiz now!

1 Velocity Velocity (m/s) Position Velocity Position 9/4/217 Motion: Acceleration Summary Last : Find your clicker! Scalars: Distance, Speed Vectors: Position velocity Speed = Distance covered/time taken v = Dx / Dt, Graphs: x vs t v vs t Day 3: Get your clickers ready! Motion Position, velocity Acceleration Reminders: HW 1 due tonight, 1pm on D2L Homework 2 available on D2L Reading quiz now! Today: Relationship between v x vs t graphs Equations of motion: Constant velocity Changing units Acceleration Equations of motion at constant acceleration. Speed velocity question 1. You are driving 6 miles per hour north. 2. You are driving 6 miles per hour. Position velocity graphs Person #1 moves away from the origin as shown Sketch position vs. velocity vs. graphs for person #2 moving away from origin (motion detector) at twice the velocity of person #1 #1 a. both give your speed, can t tell your velocity. b. 2. gives speed, 1. gives velocity. c. both are giving your velocity. d. 2 gives velocity, 1. gives your speed. #1 Relationship between position vs graph velocity vs graph Dx Dt (t i, x i ) (t f, x f ) Change in position (Dx) Velocity = Time taken (Dt) = Gradient (slope) of position/ graph Relationship between position vs graph velocity vs graph What does velocity graph look like? Velocity is the slope of position graph What does it look like between 1s? 1 1 (s) (s) 1

2 Velocity (m/s) Velocity (m/s) 9/4/217 Relationship between position vs graph velocity vs graph Velocity is the slope of position graph Relationship between position vs graph velocity vs graph Velocity is the slope of position graph 1 1 What about velocity between 1s 3s? a) Negative, decreasing magnitude b) Negative, Increasing magnitude c) Negative, constant magnitude d) Positive, constant magnitude e) Can t tell from info given 1 (s) Velocity at 2 s is: a) 1 m/s b) 1 m/s c).5 m/s d).5 m/s e) 1/6 m/s 1 (s) (s) (s) 1 1 Relationship between position vs graph velocity vs graph Velocity is the slope of position graph (x i =1m, t i =1s) (x f =m, t f =3s) (s) Equations of motion Several ways to describe motion so far: 1. Words 2. Arrows (vectors) numbers (scalars) 3. Graphs 4. Equations Dx x f x i Velocity (v) = = Rearrange: Dt x f x i = v( t f t i ) x f = x i v( t f t i ) t f t i Now let t i = s so x i = x. Note: When using symbols vector quantities like x v are differentiated from scalars either by using bold type or by underlining the symbol. x f = x o v t f The subscript f is now unnecessary so we can write: x = x o v t Motion at constant velocity x(t) = x vt Practice question x(t) = x vt 2m/s your position at t depends on: Where you started, How fast in what direction you re going, How long you ve been going 1 Position (m) I start 1m to the right of the origin at t=. I walk to the right for 3s at 2m/s. What is my position at 3s? (Define positions to the right of the origin as positive) a. 1m b. 4m c. 5m d. 3m e. 7m 2

3 position 9/4/217 Break to discuss units If you drive 6 miles/hour, that s a speed. It s also 1 mile/minute It s also 1/6 mile/s Physics units: meters/second (m/s) There are 16 meters in a mile. If you drive 6 miles/hour, how fast is this in m/s? a) 6 m/s b) 16 m/s c) 27 m/s d) 27 m/s e) 16 m/s How did you get that? We want to change the units but keep the answer (speed) the same Remember 2 things: Multiply any answer by 1 it doesn t change 16m = 1mile 16m 1 mile = 1 We have speed in mi/hr, we want m/s so: How did you get that? We want to change the units but keep the answer (speed) the same Remember 2 things: Multiply any answer by 1 it doesn t change 16m = 1mile 16m 1 mile = 1 Speed = 6mi hr First change miles to meters Then change hours to seconds Speed = 6mi hr Walking man moves according to the position graph, below. At which is Walking Man slowing down (speed decreasing)? a) A only b) B only c) C only d) A C e) A, B, C A B C Equations when velocity is changing What if velocity is changing? Accelerating Acceleration (a) is a VECTOR Units = m/s = m/s 2 s a = Gradient of a velocity vs graph Change in velocity (Dv) = Time taken (Dt) v f v i = t f t i 3

4 Velocity (m/s) 9/4/217 Graph shows the velocity of a car as a function of. What is its acceleration? a..25m/s 2 b..25m/s 2 c..4m/s d..25m/s e..65m/s 2 5 Equations when velocity is changing What if velocity is changing? Accelerating Acceleration (a) = Rearrange: v f v i t f t i v f v i = a( t f t i ) v f = v i a( t f t i ) Now let t i = s so v i = v drop the f subscript v = v a t 8 5 s 1 s 15 s 2 s Motion at constant acceleration your velocity at t depends on v(t) = v at Your velocity when you started, How fast in what direction you are accelerating, How long you ve been going What about position at constant acceleration? So far: x = x vt (a = ) (1) v = v at (a = constant) (2) From (1) : x = x v average t (if a ) (3) v average = v ½ (change in velocity) a = change in velocity / taken v average = v ½ at (4) Substitute (4) into (3) x = x (v ½ at)t x = x v t ½ at 2 Position at constant acceleration x(t) = x v t ½ at 2 your position at t depends on Where you started, How fast in what direction you started going, How fast in what direction you re accelerating, How long you have been going Equations of motion: Motion at constant velocity: x = x vt Motion at constant acceleration: v = v at x = x v t ½ at 2 Note: These equations only work if acceleration is CONSTANT. 4

5 Acceleration position Velocity 9/4/217 A car accelerates at a steady rate from stationary along a straight road. Sketch position, velocity acceleration as a function of Hint: a is gradient of v vs t v is gradient of x vs t 5

Physic 231 Lecture 3. Main points of today s lecture. for constant acceleration: a = a; assuming also t0. v = lim

Physic 231 Lecture 3. Main points of today s lecture. for constant acceleration: a = a; assuming also t0. v = lim Physic 231 Lecture 3 Main points of today s lecture Δx v = ; Δ t = t t0 for constant acceleration: a = a; assuming also t0 = 0 Δ x = v v= v0 + at Δx 1 v = lim Δ x = Δ t 0 ( v+ vo ) t 2 Δv 1 2 a = ; Δ v=