NOTES 2.1: One-Dimensional Motion · •Define Displacement. •Determine a time interval. •Define Velocity. •Differentiate between Speed and Velocity. •Define Acceleration.

BELL RINGER:

• Define Displacement.

• Define Velocity.

• Define Speed.

• Define Acceleration.

• Give an example of constant acceleration.

• What does the below equation tell us?

𝑣 =∆𝑑

∆𝑡

NOTES 2.1: ONE-DIMENSIONAL MOTION

Physics Honors I

OBJECTIVES:

• Define Displacement.

• Determine a time interval.

• Define Velocity.

• Differentiate between Speed and Velocity.

• Define Acceleration.

• Relate velocity and acceleration to the motion of an object.

• Create distance-time graphs, velocity-time graphs, and acceleration-time graphs.

ACTIVE PHYSICS REFERENCE:

• Average velocity and Speed – Chapter 1, Section 3, Page 37-41

• Graphing Velocity – Chapter 1, Section 3, Page 41-43

• Acceleration – Chapter 1, Section 4, Page 58-62

• Acceleration – Chapter 4, Section 1, Page 353-354

• Graphing Acceleration – Chapter 1, Section 4, Page 63-64

FURTHER LEARNING:

• Khan Academy – Displacement

https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/a/what-is-displacement

• Khan Academy – Average Velocity (there are several videos on the left-hand side. It comes with video explanation but also some very good reading).

https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/v/calculating-average-velocity-or-speed

• Khan Academy – Accelerationhttps://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/v/acceleration

FURTHER LEARNING:

• Study.com (Video) – Acceleration:

http://study.com/academy/lesson/what-is-acceleration-definition-and-formula.html

• Bozeman Science (Video) – Position vs Time Graph I:

https://www.youtube.com/watch?v=ohYQMEhl5Cc&list=PL495D7879B0AB8AB7&index=1

• Bozeman Science (Video – Position vs Time Graph 2:

https://www.youtube.com/watch?v=ohYQMEhl5Cc&list=PL495D7879B0AB8AB7

POSITION:

• In physics, we love to precisely describe the motion of an object.

• But to describe an object's motion, we have to first be able to describe its position—where it is at any particular time.

• More precisely, we need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame.

DISTANCE VS DISPLACEMENT:

DISTANCE VS DISPLACEMENT:

• Distance - a measurement of the length between two points

• Distance is the same as distance traveled.

• Distance is a scalar.

• Displacement - overall change of position.

∆𝑑 = 𝑑𝑓 − 𝑑𝑖

• Displacement is only concerned with the starting position and the final position.

• Displacement is a vector.

DISTANCE VS DISPLACEMENT:

Example:

• My posters on the wall does not seem symmetric with the other posters which agitates me to no end.

• I move it 8” to the right and realize it is too close to the other poster.

• I move it 6” to the left and realize it is too far from the other poster.

• I move it 2” to the right and find that it seems perfect.

• How much distance did my poster cover and how much was it displaced?

• In this scenario, do we actually care about the total distance the poster covered?

SPEED:

• Speed is the magnitude of velocity.

• Another way to think of speed is the absolute value of velocity.

• Speed is a scalar.

• Speed is the total distance per the total time.

𝑆𝑝𝑒𝑒𝑑 =𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒

𝑣 =𝑑

𝑡

VELOCITY:

• Velocity is a vector.

• Velocity is the total displacement per the total time.

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒

Ԧ𝑣 =𝑑𝑓 − 𝑑𝑖𝑡𝑓 − 𝑡𝑖

Ԧ𝑣 =∆𝑑

∆𝑡

VELOCITY:

Ԧ𝑣 =∆𝑑

∆𝑡

EXAMPLE 1:

You are traveling at 35 mph (about 50 ft/s) and your reaction time is 0.2s. Calculate the distance you travel during your reaction time.

∆𝑑 = 𝑣 𝑥 ∆𝑡

𝑣 = 50𝑓𝑡

𝑠∆𝑡 = 0.2 𝑠

∆𝑑 = (50𝑓𝑡

𝑠) (0.2 s)

∆𝑑 = 10 𝑓𝑡

CHECKPOINT 1:

1. If you drive a distance of 640 km (400 mi) in 8 h, what is your average speed?

2. In an automobile collision, it was determined that a car traveled 150 ft before the brakes were applied.

A) If the car had been traveling at the speed limit of 40 mph (60 ft/s), what was the driver’s reaction-time (time it took to apply the brakes?

B) Witnesses say that the driver appeared to be under the influence of alcohol. Does your reaction-time data support the witnesses testimony?

DISTANCE VS TIME – GRAPHING VELOCITY:

• The slope of the line on a distance vs. time graph is velocity.

DISTANCE VS TIME – GRAPHING VELOCITY:

• Therefore, you can use the familiar equation of

𝑠𝑙𝑜𝑝𝑒 =𝑅𝑖𝑠𝑒

𝑅𝑢𝑛

to find the velocity on a distance vs. time graph.

DISTANCE VS TIME – GRAPHING VELOCITY:

DISTANCE VS TIME – GRAPHING VELOCITY:

• A person is at rest. As time increase, there is no change in the position of the person. The person is standing still.

• The graph of a person at rest is a horizontal line with a slope of zero – representing a speed of zero.

DISTANCE VS TIME – GRAPHING VELOCITY:

• A person is traveling at a slow speed. As time increases, there is a small change in position.

• A slow speed has a gradual slope.

• Any time there is a steady rate of change (i.e. Linear) that is known as CONSTANT VELOCITY.

DISTANCE VS TIME – GRAPHING VELOCITY:

• A person is traveling at a fast speed. As time increases, there is a greater change in the position.

• A fast speed has a steep slope.

• Is this constant velocity?

DISTANCE VS TIME – GRAPHING VELOCITY:

• A person is traveling in the opposite direction of the person in the previous graphs. As time passes, the change in position is in the opposite direction.

• Is this constant velocity?

DISTANCE VS TIME – GRAPHING VELOCITY:

• A person is changing speed. As time passes, the change in position is increasing for each second.

• Notice that a changing speed is a curve on a distance-time graph.

• Is this constant velocity?

EXAMPLE 2 – GRAPHING VELOCITY:

• Graph the following:

• You stroll to an ice-cream stand 1.2 km away from your house, walking at a steady pace and arriving there in 20 minutes.

• It takes 5 minutes to eat your ice cream, and then you head back home at the same steady speed you were traveling before.

• Half-way home, you pause for 5 minutes to watch a construction project before walking the rest of the way at the same steady speed.

EXAMPLE 2 – GRAPHING VELOCITY:

CHECK POINT 2 – GRAPHING VELOCITY:

• Using the Graph, answer the following.

3. How far did you walk?

4. How fast did you walk?

5. What was your average speed for the entire trip?

6. How fast, and in what direction were you going on the way to the ice-cream stand?

7. What overall change in your position occurred over the entire trip?

ACCELERATION:

• Acceleration essentially is the rate at how fast something speeds up or slows down.Average Acceleration (𝒂𝒂𝒗𝒈 ):

𝒂𝒂𝒗𝒈 =𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚

𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆

𝒂𝒂𝒗𝒈 =v𝟐−v𝟏

t𝟐− t𝟏=

∆v

∆t

• Acceleration has the SI unit of meters per second per second (m/s2)

• Acceleration is a vector and does has both a magnitude and direction.

ACCELERATION:

ACCELERATION AND CONSTANT VELOCITY:

Average Acceleration (𝒂𝒂𝒗𝒈 ):

𝒂𝒂𝒗𝒈 =v𝟐−v𝟏

t𝟐− t𝟏=

∆v

∆t

• From the above equation, you can see that when there is NO CHANGE IN VELOCITY, then there is NO ACCELERATION.

ACCELERATION:

• Scenario: Your planes from Jacksonville (JAX) lands in Atlanta (ATL) in Concourse B-14. Your flight to Paris departs from Concourse F-11. So you have to take the train from Concourse B to Concourse F.

• You get on the train, there are no sitting position so you have to stand and don’t have anything to hold on to. What happens to your body when the train starts moving?

• You feel pushed back, right?

• What happens when the train has reached its maximum speed? Can you stand up straight and even walk normally?

ACCELERATION:

• Positive Acceleration – Speeding up

• Negative Acceleration – Slowing down (Deceleration)

EXAMPLE 3:

• At the start of a race, a toy car increases speed from 0 m/s to 5.0 m/s as the clock runs from 0 s to 2.0 s. Find the acceleration of the toy car.

𝒂𝒂𝒗𝒈 =v𝟐 − v𝟏t𝟐 − t𝟏

𝒂𝒂𝒗𝒈 =(𝟓. 𝟎

𝒎𝒔 ) − (𝟎

𝒎𝒔 )

𝟐. 𝟎 𝒔 − 𝟎 𝒔

𝒂𝒂𝒗𝒈 = 𝟐. 𝟓 ൗ𝒎𝒔𝟐

ACCELERATION - GRAPHING:

• The slope of a Velocity-Time Graphs is Acceleration.

ACCELERATION - GRAPHING:

• Again, you can use the familiar equation of

𝑠𝑙𝑜𝑝𝑒 =𝑅𝑖𝑠𝑒

𝑅𝑢𝑛

except this time it is to find the acceleration on a velocity vs. time graph.

AUTOMOBILE AT REST:

AUTOMOBILE WITH CONSTANT VELOCITY:

AUTOMOBILE WITH CONSTANT ACCELERATION:

CHECK POINT 4:

8. Describe the motion of a ball as it rolls up a slanted driveway. The ball starts at 2.50 m/s, slows down for 5.00s, stops for an instant, and then rolls back down at an increasing speed. The positive direction is chosen to be up the driveway, and the origin is at the place where the motion begins.

(a)What is the sign of the ball’s acceleration as it rolls up the driveway?

(b)What is the magnitude of the ball’s acceleration as it rolls up the driveway?

HELPFUL TACTICS I:– DO YOU UNDERSTAND THE PROBLEM

• Can you explain the problem? Having the capability to explain a problem is the best test of your ability to understand a problem.

• To help understand a problem, write down any given data, with units.

• Identify the unknowns.

• Attempt to find any connection between the unknown and the given data.

HELPFUL TACTICS 2:– ARE THE UNITS OKAY?

• Be sure to use a consistent set of units, and convert as needed.

• Make sure the units to your final solution match. Such as the SI unit for velocity is meters per seconds (m/s); therefore, if solving for velocity than the units should also match meters per seconds (m/s).

HELPFUL TACTICS 3:– IS YOUR ANSWER REASONABLE?

• Does your answer make sense, or is it too large or too small?

• For instance, if you calculate your cars velocity to be going faster than the speed of light than your answer is far too large.

HELPFUL TACTICS 4:– READING A GRAPH

• Review how to read a graph if you’re having any issues.

• Also, make sure you know the units being used anytime with using a graph. The graph does not make sense if you don’t know what units are being used.

• Graphing is a very important tool in math and physics so it is very beneficial to make sure you understand how to graph well. Pay attention in algebra, and calculus.

HELPFUL TACTICS 5:– AN ACCELERATION’S SIGN

If the sign of the velocity and acceleration of a particle are the same, the speed of the particle increases. If the signs are opposite, the speed decreases.

FUN VIDEO – SUPER SPEED:

EXIT TICKET 1:

9) You drive a beat-up pickup truck along a straight road for 8.4 km at 70 km/h, at which point the truck runs out of gasoline and stops. Over the next 30 minute, you walk another 2.0 km farther along the road to a gasoline station.

(a) What is your overall displacement from the beginning of your drive to your arrival at the station?

(b) What is the time interval ∆𝑡 from the beginning of your drive to your arrival at the station?

(c) What is your average velocity 𝑣𝑎𝑣𝑔 from the beginning of your drive to your

arrival at the station?

EXIT TICKET 2:

10) Describe how constant velocity affects acceleration?

11) What is constant acceleration?

12) The slope of the line on a distance vs time graph represents what?

13) The slope of the line on a velocity vs time graph represents what?

14) A race car’s velocity increases from 4.0 m/s to 36 m/s over a 4.0s time interval. What its average acceleration?