One Dimensional Motion Physics I

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Speed and Velocity MHS Physics

In The Grand Scheme of Things… __________ – the study of the motion of objects and the related concepts of force and energy__________ – the study of the motion of objects and the related concepts of force and energy –__________ – the description of how objects move Linear Motion – motion in 1-DLinear Motion – motion in 1-D Projectile Motion – motion in 2-DProjectile Motion – motion in 2-D –__________ – deals with force and why objects move as they do

Magnitude Size

Scalars (Magnitude)Vector (Magnitude and Direction) Distance (20 m)Displacement (20 m, North or +20 m) Speed (20 m/s)Velocity (20 m/s, North or +20 m/s) Mass (20 kg)Acceleration (+20 m/s 2 ) Time (20 seconds) Scalar – Quantity with magnitude only VectorVector – Quantity with magnitude and direction

Distance vs. Displacement Displacement can be negative! Distance Displacement or change in position Initial position, x o Final position, x (x-x o =  x) Cutnell & Johnson

Distance vs. Displacement

Distance and Displacement For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W. Net displacement D is from the origin to the final position: What is the distance traveled? 20 m !! 12 m,W D D = 4 m, W x 8 m,E x = +8 Author: Tippens, P. (2007)

Speed, Velocity and Acceleration speed – __________ traveled per unit of timespeed – __________ traveled per unit of time (average speed) velocity – speed in a given __________velocity – speed in a given __________ –displacement per unit of time (average velocity) acceleration – change in __________ per unit of timeacceleration – change in __________ per unit of time (average acceleration)

Definition of Speed Speed is the distance traveled per unit of time (a scalar quantity). s = = dtdt 20 m 4 s v = 5 m/s Not direction dependent! A B d = 20 m Time t = 4 s Author: Tippens, P. (2007)

Definition of Velocity Velocity is the displacement per unit of time. (A vector quantity.) v = 3 m/s East Direction required! A B d = 20 m Time t = 4 s x=12 m Author: Tippens, P. (2007) North East

Constant Speed Ticker Tape Diagrams: Which diagram represents a faster constant speed?

What is the difference in the car’s average velocity in part a) and part b)? Average velocity Average Speed = Cutnell & Johnson t = s Means change in, so subtract!

Example 1. A runner runs 200 m, east, then changes direction and runs 300 m, west. If the entire trip takes 60 s, what is the average speed and what is the average velocity? Recall that average speed is a function only of total distance and total time: Total distance: s = 200 m m = 500 m Avg. speed 8.33 m/s start s 1 = 200 ms 2 = 300 m Author: Tippens, P. (2007)

Example 1 (Cont.) Now we find the average velocity, which is the net displacement divided by time. In this case, the direction matters. x o = 0 t = 60 s x 1 = +200 mx f = -100 m x 0 = 0 m; x f = -100 m Direction of final displacement is to the left as shown. Average velocity: Note: Average velocity is directed to the west. Author: Tippens, P. (2007)

Example 2. A sky diver jumps and falls for 625 m in 14 s. After chute opens, he falls another 356 m in 142 s. What is average speed for entire fall? 625 m 356 m 14 s 142 s A B Average speed is a function only of total distance traveled and the total time required. : Total distance/ total time: Author: Tippens, P. (2007)

Average velocity Average Speed = From a Graphical View: When finding the average velocity for each interval, what feature of the graph are you calculating? (Math term) Cutnell & Johnson

Interpret the motion of the object in the graph below. 1.How fast (average velocity) is the object traveling in each interval of time? How can this be determined? 2.What is the average velocity of the entire trip? 3.What is the average speed of the entire trip?

During which time intervals did it travel in a positive direction? During which time interval did it travel in a negative direction? 0-10 sec, sec sec Notice the correlation between the signs of the slopes and the direction it is traveling in each time interval +

Average Speed and Instantaneous Velocity The instantaneous velocity is the magnitude and direction of the speed at a particular instant. (v at point C) The instantaneous velocity is the magnitude and direction of the speed at a particular instant. (v at point C)  The average speed depends ONLY on the distance traveled and the time required. A Bs = 20 m Time t = 4 s C Author: Tippens, P. (2007)

What direction (pos. or neg.) is the object traveling during 0-1 sec? When is the object traveling in a neg. direction? What is the object doing during the 1-2 second interval? What is the average speed from 2-3 seconds? What is the instantaneous speed at 3.5 seconds? Velocity vs. time graph Positive Velocity indicates positive displacement s m/s 2

Average Acceleration The rate of change in instantaneous velocity, either magnitude, direction, or both. Acceleration can be either be positive or negative – vector quantity

Three Ways to Accelerate Hewitt, P. Conceptual Physics.

Positive and Negative Acceleration +a -a Average Acceleration is a change in velocity over time Cutnell & Johnson

Positive and Negative Acceleration x0x0 x -a x0x0 x +a v0v0 v0v0 v v

Example 3 (No change in direction): A constant force changes the speed of a car from 8 m/s to 20 m/s in 4 s. What is average acceleration? Step 1. Draw a rough sketch. Step 2. Choose a positive direction (right). Step 3. Label given info with + and - signs. + v 1 = +8 m/s t = 4 s v 2 = +20 m/s Author: Tippens, P. (2007)

Example 3 (Continued): What is average acceleration of car? Step 4. Recall definition of average acceleration. + v 1 = +8 m/s t = 4 s v 2 = +20 m/s Author: Tippens, P. (2007) 2

Example 4: A wagon moving east at 20 m/s encounters a very strong head-wind, causing it to change directions. After 5 s, it is traveling west at 5 m/s. What is the average acceleration? (Be careful of signs.) Step 1. Draw a rough sketch. + Step 2. Choose the eastward direction as positive. v o = +20 m/s v f = -5 m/s Step 3. Label given info with + and - signs. Author: Tippens, P. (2007)

Example 4 (Cont.): Wagon moving east at 20 m/s encounters a head-wind, causing it to change directions. Five seconds later, it is traveling west at 5 m/s. What is the average acceleration? Choose the eastward direction as positive. Initial velocity, v o = +20 m/s, east (+) Final velocity, v f = -5 m/s, west (-) The change in velocity,  v = v f - v 0  v = (-5 m/s) - (+20 m/s) = -25 m/s Choose the eastward direction as positive. Initial velocity, v o = +20 m/s, east (+) Final velocity, v f = -5 m/s, west (-) The change in velocity,  v = v f - v 0  v = (-5 m/s) - (+20 m/s) = -25 m/s Author: Tippens, P. (2007)

Example 4: (Continued) a avg = = vtvt v f - v o t f - t o a = -25 m/s 5 s a = - 5 m/s 2 + v o = +20 m/s v f = -5 m/s East  v = (-5 m/s) - (+20 m/s) = -25 m/s Author: Tippens, P. (2007)

A student walks 3 meters, North and then 4 meters, South in 6 seconds. What is the average velocity? m/s, North m/s, South m/s, North m/s, South

The sign of the velocity of an object represents the 1.The magnitude 2.The direction 3.The acceleration 4.The speed

Interpret the graph below and draw a position vs. time graph and an accel. vs. time graph. When is the object accelerating? How can this be determined? +a 0 -a TΔxΔx

Corresponding Position vs. Time Graph

Corresponding Acceleration vs. Time Graph

What is the instantaneous speed of the object at point B? m/s 3.+2 m/s m/s m/s

1. When was he traveling in a positive direction? 2. When was he traveling in a negative direction? 3. When was he at rest? 4. During what time intervals did he travel at a constant velocity? 5. During what time interval did he travel the greatest distance? 6. When does he have a positive acceleration? 7. When is he increasing his speed? Decreasing his speed? 8. What is the average acceleration during interval A? 9. What is the instantaneous acceleration at 2.5 seconds? Velocity vs. Time Graphs A B C E D F G H

Describe the motion of the object. Initial position is 0.0 m. 5.0

Summary: Corresponding Shapes of Motion Graphs with Constant Acceleration dv dv dv dv

Which graph best matches the statement?

Graph Shapes Linear; y = mx +bQuadratic: y = x 2 Inverse: y = 1/x Inverse Square : y = 1/x 2

Credits: Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons. Foxtrot Cartoon: Bill Amend. Received from 2007 AP Conference. Hewitt, P. [Illustrations]. Conceptual Physics. Nave, R. (2010). Hyperphysics.[Illustration]. Permission granted to use illustrations. Retrieved from Tippens, P. (2007). Chapter 6A Acceleration [PowerPoint Slides]. Received from 2007 AP Conference.