Summary of motion graphs Object is moving to the right (in positive direction) v = 0 a = 0
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1 Summary of motion graphs Object is moving to the right (in positive direction) Object at rest (not moving) Position is constant v (m/s) a (m/s 2 ) v = 0 a = 0 Constant velocity Position increases at constant rate v (m/s) a (m/s 2 ) Velocity is constant a = 0 Constant acceleration Slowing down slope decreases Speeding up slope increases v (m/s) a (m/s 2 ) Speeding up Slowing down Speeding up; a is positive Slowing down; a is negative
2 Summary of motion graphs Object is moving to the left (in negative direction) Object at rest (not moving) x (m) Position is constant v (m/s) a (m/s 2 ) v = 0 a = 0 Constant velocity x (m) Position decreases at a constant rate v (m/s) Velocity is constant and a (m/s 2 ) negative a = 0 Constant acceleration x (m) Speeding up slope increases Slowing down slope decreases v (m/s) a (m/s 2 ) Slowing down; moving left Speeding up; moving left Slowing down; a is positive Speeding up; a is negative
3 What is a Position vs. Time or x vs t motion graph? Position is the distance of the object from zero (+ or -). x vs. t graph plots the object s positions at different times (see dot diagram). (also called Displacement vs. Time graphs on MCAS) What is a Distance vs. Time or d vs t motion graph? Distance is always positive (a scalar). d vs. t graph plots the object s distance from zero at different times, ignoring direction of motion. Direction of motion is unknown
4 What is a Velocity vs. Time or v vs t motion graph? Velocity is speed and direction of motion. v vs. t graph plots the object s velocities (+ or -) at different times. What is a Speed vs. Time or s vs t motion graph? Speed is always positive (a scalar). s vs. t graph plots the object s speed at different times, ignoring direction of motion. Direction of motion is unknown
5 Position is plotted on the y-axis in this case. Position has units of distance (e.g., m, mi, ft) On a Position vs. Time graph, what are the units on the y-axis? (m) On a Velocity vs. Time graph, what are the units on the y-axis? Velocity is plotted on the y-axis in this case. Velocity has units of distance divided by time (e.g., m/s, mi/h, ft/min) v (m/s)
6 What information does a Position vs. Time give you about the motion? (also called Displacement vs. Time graphs on MCAS) 1. Read the object s positions at different times. 2. Find slope to get velocity, which may or may not be constant. Position (m) What information does a Distance vs. Time give you about the motion? 1. Read the object s distance at different times. 2. Find slope to get speed, which may or may not be constant. Direction of motion is unknown
7 What information does a Velocity vs. Time give you about the motion? 1. Read the object s velocity at different times. 2. Find slope to get acceleration, which may or may not be constant. What information does a Speed vs. Time give you about the motion? 1. Read the object s speed at different times. 2. Find slope to get acceleration, which may or may not be constant. Direction of motion is unknown
8 How do you find average velocity from a Position vs. Time graph? run 4 s rise 20 m (also called Displacement vs. Time graphs on MCAS) To find average velocity from an x vs. t graph, find the slope. Example: Find the average velocity during the first 4 seconds of motion. rise 20m vavg = slope = = = 5 m / s run 4s Ave. velocity during 0-4s is 5m/s to the right. Example: What is the average velocity during 5-6s? : 0 m/s, because the slope is zero.
9 Direction of motion is unknown: speed is a scalar How do you find average speed from a Distance vs. Time graph? To find average speed from a d vs. t graph, find the slope. Example: Find the average speed of the Biker. rise 15m savg = slope = = = 15 m / s run 1s Example: Find the average speed of the Runner. rise 20m savg = slope = = = 5 m / s run 4s Steeper slope on d vs. t graph means faster speed!
10 How do you find average acceleration from a Velocity vs. Time graph? rise 8m/s run 3 s To find average acceleration (or a ) from a v vs. t graph, find the slope. Example: Find the average acceleration during 7-10 s of motion. rise 8 m / s a = slope = = = 2.7 m / s run 3s Acceleration is negative and velocity is positive (opposite directions) object is slowing down, as seen on graph! 2
11 Why does a straight line on a Position vs. Time graph mean constant velocity? Constant velocity means constant speed and constant direction (moving in a straight line). Constant speed means the object travels equal distances in equal times. On the graph, the object travels 10 m every 5 s equal distances in equal times, which looks like a straight line. Position (m) What information does an Acceleration vs. Time (or a vs. t ) graph give you about the motion? An a vs. t graph tells you the acceleration of an object at different times. In this course, you deal with constant acceleration which is a flat line on an a vs. t graph. Acceleration (m/s 2 ) a = 0.4 m/s 2 a = 0 a = m/s 2
12 What does the slope mean on: Because we are plotting vector quantities, slopes are vectors too and include direction. Position vs. Time graph Velocity vs. Time graph Who is moving the slowest? Explain. This is a d vs. t graph (or Distance vs. Time). The slope on a d vs. t graph is speed. Steepest slope fastest speed Lowest slope slowest speed Walker has the slowest speed.
13 What does the slope mean on: Distance vs. Time graph Speed vs. Time graph distance vs. time speed vs. time Speed only Acceleration (speeding up or slowing down only no direction) In what direction are the people moving? Explain. This is a d vs. t graph (or Distance vs. Time). Distance is a scalar and does not give information about direction. This graph does not provide information to answer this question.
14 Describe the motion on this graph. This Position vs. Time graph shows that the: Object starts at a position of 0 Moves to the right (Because position is increasing) Speeds up (Because the slopes are increasing) Tangent slopes are getting steeper speeding up Sketch a Velocity vs. Time graph for the following Position vs. Time graph. Object is moving to the right (position increases). So, Velocity is always positive. Object is speeding up (slopes increase). So, Velocity increases.
15 Describe the motion on this graph. This Position vs. Time graph shows that the: Object starts at a positive position Moves to the left (Because position is decreasing) Slows down (Because the slopes are decreasing) Tangent slopes are getting less steep slowing down Sketch a Velocity vs. Time graph for the following Position vs. Time graph. Position decreases, so velocity is always negative. Speed increases because tangent slopes increase.
16 Sketch a Position vs. Time graph of an object moving to the left and slowing down. Sketch a Position vs. Time AND Velocity vs. Time graphs of an object moving right and slowing down to a stop.
17 Sketch a Position vs. Time AND Velocity vs. Time graphs of an object moving in the negative direction at constant velocity. Sketch a Position vs. Time AND Velocity vs. Time graphs of an object moving in the positive direction and slowing down to a stop.
18 A truck accelerates from rest, moving North. Sketch a Position vs. Time based on its Acceleration vs. Time graph of its motion. A truck accelerates while moving South. Sketch a Position vs. Time based on its Acceleration vs. Time graph of its motion. Acceleration is constant and positive. Because the truck speeds up moving North (+), Velocity and Acceleration are both positive (same direction). Position-Time graph slopes must be positive and increasing. Acceleration is constant and positive. Because the truck is moving South (-), it is slowing down. Position-Time graph slopes must be negative and decreasing.
19 Describe this motion in words. 1 2 Describe this motion in words. 1. Object moves left (positions decrease) and slows down (slopes decrease). 2. Object moves right (positions increase) and speeds up (slopes increase) Object moves right (positions increase) and slows down (slopes decrease). 2. Object moves left (positions decrease) and speeds up (slopes increase).
20 Which time interval shows positive acceleration, and which shows negative acceleration? This is a Velocity-Time graph. Slope means acceleration. Z: Acceleration is positive because the slope is positive. W: Acceleration is negative because the slope is negative. Which time interval(s) show a = 0 This is a Velocity-Time graph. Slope means acceleration. Time intervals W and Y show zero acceleration because the slope is zero.
21 Describe the car s motion between Time 1 and Time 2. This is a Position-Time graph. Slope means velocity. Car is moving in the positive direction (position is increasing). Car is moving at constant speed (slope is constant). How far does the object travel during s (segment B)? v (m/s) How far means displacement x. During B, the velocity is constant. To find displacement, use x= v t avg t = 30s 10 s = 20s, and v = 20 m/s. Then, m x= vavg t = 20 ( 20s) = 400m s
22 Draw a Position-Time graph of a ball thrown straight upward. Assume up is positive and there is no air resistance. Draw a Position-Time graph of a ball thrown straight upward. Assume up is positive and there is no air resistance. Ball has a positive initial velocity (going up) and slows down to a stop at 2 s. Then, the ball has a negative velocity and speeds up. Slope is constant because free-fall acceleration is a constant -10m/s/s. Ball has a positive initial velocity and slows down to a stop at 2 s. Position increases as it moves up, slopes decrease to flat. Then, the ball has a negative velocity and speeds up. Position decreases as it moves down, slopes increase. x (m)
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