General Physics I: Day 3Constant Acceleration and Freefall

Download the equation sheet (under Handouts). You’ll also get a fresh one at each exam

Have you read the MasteringPhysics grading scheme? How can you lose credit on a homework problem?

A) Opening a hint

B) Doing the problems out of order

C) Submitting a wrong answer

D) Viewing the title of a hint

E) More than one of these

→ means no bonus points

→ huh?

→ Yep! 3% each*

→ free!

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Your Time Spent

How much time did you spend doing the pre-class work for tomorrow's class?

~0% → Less than 20 minutes

~12% → 20-30 minutes

~30% → 30-40 minutes

~24% → 45-60 minutes

~34% → More than an hour

50 people did the Warm Up

4Warm-Up: Avg. Vs. Inst. PlotsWhich of the following arrows correspond to a time at which the instantaneous velocity is greater than the average velocity over the time interval shown?

14% 0% 74% 12%

Velocity vs. Time Plots

Not as much information as a position vs. time plot

Again, (+) or (-) indicate the direction, in this case the direction of motion (right/left or up/down).

On this plot, the slope is the acceleration

These are harder to understand, but doing so can really help separate the ideas of velocity and acceleration.

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Velocity vs. Time Example

What is happening here? What could it be?

(think on this for amoment)

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If the velocity of a car is non-zero, can the acceleration of the car be zero?

A) Yes, and I can give an example.

B) Yes, but I can’t tell you why.

C) No, and I can tell you why not.

D) No, but I can’t tell you why not.

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(x)

(t)

Can an object have a non-zero acceleration if it has a zero velocity?

A) Yes, and I have an example.

B) Yes, but I can’t think of an example.

C) No, and I can tell you why.

D) No, but I’m not sure why.

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(x)

(t)

A car is traveling on and east-west highway. Suppose we choose the positive x direction to be east. In which of the following situations is the average acceleration of the car negative?

Initial motion Motion at some later timeA) 10 m/s east 30 m/s east B) 10 m/s west 30 m/s westC) 30 m/s east 10 m/s eastD) 30 m/s west 10 m/s westE) More than one of the above…

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(x)

(t)

Velocity vs. Time Plots

Slope at any pointtells us the acceleration.

During what segment is the acceleration largest?

How far does it go betweentime 5.0 s and 7.0 s?

40 m/s for 3 seconds… 120 meters!

The area under the function line tells us Δx.

To find the displacement, integrate !

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Analytic Methods

As we know, uniform motion means:

This is just (Distance) = (Rate) x (Time)

How about for average acceleration:

Sometimes we just put t instead of Δt.

Rearranged:

f ix x v t

x xv a t

xf xi xv v a t

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Submitting Images: YES!

13Submitting Images: Please, no.

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Worked-Example: Dragster

Acceleration?(assumed constant)

Average speed?

Final speed?

15Worked-Example: DerivationsLook up and explain the derivations of

and

16Worked-Example: Derivations

17Worked-Example: Reversed AccelCould the same problem have been solved using a negative acceleration? Explain.

~30% → Yes, exactly the same problem

~70% → No, or it would be a different problem

18Worked-Example: Reversed AccelCould the same problem have been solved using a negative acceleration? Explain.

19Deriving Kinematics EquationsStart from our assumption: is constant

From there we use calculus to figure out how velocity and position must behave…

f

i

t

x x

t

v a dt f

i

t

x

t

x v dt

20Motion With Constant Acceleration

Four incarnations of the same idea… all about how , , , , , and relate.

If is constant, pick one that is convenient

Critical: Lots of vectors here!

212

f x xi xx x v t a t

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f i xf xix x v v t2 2 2 xf xi xv v a x

xf xi xv v a t

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Problem Solving Issues

The two most dangerous paths in physics:• Memorizing an exact recipe for solving it.• Searching for the "right" formula and then just

plugging in the numbers.

Even more dangerous because you may have had great success with these before

I am going to demand that you understand why as well as how.

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Warm-Up: Hitting The Wall

Estimate the acceleration you subject yourself to if you walk into a brick wall at normal walking speed.

Walking speeds Elapsed times:1, 1.2, 1.3, 1.8, 2.2 m/s 10 min

2, 4, 10 ft/s 30 sec3, 4 mph 2 sec

1 sec0.5 sec0.25 sec0.1 sec

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Warm-Up: Hitting The Wall

~75% → Gave a non-zero answer

“With the average human walking speed being 5[km/h] and estimated time to slow upon impact being 1 sec, I estimate my acceleration to be -1.4m*s^-2. I used the equation for average acceleration being equal to the change in x-component velocity [0 m/s - 1.389 m/s] divided by the change in time [1-0 s].”

Math is good, speed is good… time is pretty long.

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Warm-Up: Hitting The Wall

“Disclaimer: Someone was mildly hurt in the experimentation of this problem.”

“The book says a brisk walk is 2 m/s and I will estimate that it 0.1s to stop. The acceleration would be (2/.1) or 20 m/s^2.”

“Initial Velocity = 2(m/s), Final Velocity = 0(m/s), Time = 0.1(s), Acceleration = -20(m/s^2) […]”

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Warm-Up: Hitting The Wall

Other questions:

Did you get the right units?

Did you decide on a sign for your answer?

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Two cars emerge side by side from a tunnel.

• Car A is traveling with a speed of +60 km/h and has a constant acceleration of +40 km/h/min.

• Car B has a speed of +40 km/h and has a constant acceleration of +60 km/h/min.

Which car is passing the other as they come out of the tunnel?

A) Car A

B) Car B

C) Neither

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Follow-up: Continuing the question. Assuming their accelerations are constant, one minute later, both cars will have the same speed (100 km/h). At that moment

A) car A is ahead of car B.

B) the two cars are again neck-and-neck.

C) car B is ahead of car A.

Remember:car A had v = +60 km/h and a = +40 km/h/min.car B had v = +40 km/h and a = +60 km/h/min.

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Coming up…Thursday (8/28) → 3.1 – 3.3

Tuesday (9/2) → 3.4 – 3.5

Thursday (9/9) → Catch up & Mini-Exam

WarmUp is due Wednesday by 10:00 p.m.

MasteringPhysics Hwk #1 due today

MasteringPhysics Hwk #2 due Sunday by 11:59 PM