Physics 2111 Unit 1 · 2021. 1. 31. · Physics 2111 Unit 1 Things for Today: Displacement, Velocity, Acceleration –graphically Displacement, velocity, acceleration - numerically

Physics 2111

Unit 1

Things for Today:▪ Displacement, Velocity, Acceleration – graphically

▪ Displacement, velocity, acceleration - numerically

▪ 1-D Kinematics with constant acceleration

▪ Free-fall

Mechanics Lecture 1, Slide 1

What we asked about


• It honestly took me a while to do the second checkpoint exercise because I get a bit

confused as to when to use certain equations. Are there key signals in word

problems that make it easier on where to start?

• I found constant acceleration to be the most difficult for me.

• for now, some of the parts seem to be easy and the problems are also easy to

solve.

• In the pre-lecture some of the integral equations were slightly confusing, but it might

just be because the videos themselves were condensed.

• Im not sure why the ball rolling down the ramp had a velocity of 3 feet/sec instead of

2 feet/sec or even 4 feet/sec.

• I remember most of the topics since when I took physics in high school I feel that I

just need to see some more examples and do practice to understand it fully.

• The rolling down the ramp question was kinda confusing. I am not sure how the

answer was 3. Is there a specfic equation to use or is it more common sense?

• I would like to discuss the relationships between the position/velocity/acceleration

graphs and how they affect each other. If there is time to review kinematic

equations that would be great as well.

• I think the constant acceleration equations were the hardest to understand.

• I found it more confusing that the equation is r = r0 + v0t + at^2/2 in the formula

sheet and not x = x0 + v0t + at^2/2 since I tend to think of r as radius and x as

distance/displacement.

• Reading graphs


Think of what the position graph would look like for someone who started 10 meters from the origin and walked away at 2 meters per second.

po

siti

on

Displacement and Velocity in One Dimension

time


Displacement (rise)

Time taken (run)


Rise

= Slope

Run

Speed = |v(t)| when moving in one direction

The v(t) vs. t plot is just theslope of the x(t) vs. t plot



Definition:

• Speed = path / time

• Average Velocity = displacement / time



A) YESB) NO

Are the plots shown at the left correctly related

The velocity vs. time plot of some object is shown to the right.

Which diagram below could be the Displacement vs. time plot for the same object?

A B C

QUESTION


QUESTION


The graph represents the position as a function of time for an object in one-dimensional motion. Identify which statement below correctly identifies the times at which the velocity of the object is greater than zero.

va) The velocity is greater than 0 at t = 0 s and t = 4 s.

b) The velocity is greater than 0 at t = 2 s.

c) The velocity is greater than 0 at t = 0 s and t = 1 s.

d) The velocity is greater than 0 at t = 3 s and t = 4 s.

e) The velocity is greater than 0 at t = 0, 1, 3, and 4 s.


Acceleration

Question

At what point on the velocity graph is the acceleration zero?

A) A

B) B

C) C

D) both A and C


A

B

C


NOTES


For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time?

A

B

Checkpoint 1

QUESTION


The graph represents the velocity as a function of time for an object in one-dimensional motion. Identify which statement below correctly describes the motion at t = 3 s

va) The object is slowing down and the acceleration is negative.

b) The object is speeding up and the acceleration is negative.

c) The object is slowing down and the acceleration is positive.

d) The object is speeding up and the acceleration is positive.

QUESTION


Which pair of these graphs could represent the same motion?

v

x v

v a

(1) (2)

(3) (4)

a) (1) and (3)

b) (2) and (3)

c) (3) and (4)

d) (1) and (2)

e) None of them

QUESTION


In which of the above graphs could the object reverse its direction?

v

x v

v a

(1) (2)

(3) (4)

a) (1)

b) (2)

c) (3)

d) (4)

e) (1) and (2)

As shown to the right, a physics student is moving to the right with the positive direction to the right. She originally is jogging at 3m/sec, but in a period of 4 seconds, she slows to a walk of 1m/sec. What is her acceleration?

QUESTION


+

a) 4.0 m/sec/secb) -4.0 m/sec/secc) 0.5m/sec/secd) -0.5 m/sec/sece) none of the above

QUESTION


As shown above, a physics student is moving to the right with the positive direction to the right. She originally is walking at 1m/sec, but in a period of 2 seconds, she speeds up to a jog of 3m/sec. What is her average acceleration?

+

a) 1.0m/sec/secb) -1.0 m/sec/secc) 4.0 m/sec/secd) -4.0 m/sec/sec e) none of the above

As shown above, a physics student is moving to the left with the positive direction to the right. She originally is walking at 1m/sec, but in a period of 2 seconds, she speeds up to a jog of 5m/sec. What is her average acceleration?

QUESTION


+

a) 2.0m/sec/secb) -2.0 m/sec/secc) 4.0 m/sec/secd) -4.0 m/sec/sec e) none of the above

QUESTION


In the above sketch, to the right is positive. A student is originally walking at 2m/sec to the right, but during a period of 2 seconds, she has reversed direction and is walking to the left at 2m/sec. What is her average acceleration during these 2 seconds?

+

a) 0.0 m/sec/secb) 2.0m/sec/secc) -2.0 m/sec/secd) 4.0 m/sec/sece) -4.0 m/sec/sec


In physics, what is the difference between “accelerating” and “deaccelerating”?

QUESTION

a) One is speeding up, the other is slowingdown.

b) One is moving to the left, the other ismoving to the right.

c) We don’t say “deaccelerating”in physics

Does “acceleration” always mean “speeding up”?

(A) Yes (B) NO

Does “positive acceleration” always mean “speeding up”?

(A) Yes (B) NO


Example Problem 1.1

The position in meters of an object moving along a straight line is given by the equation

x = 6m + 9.0m/sec2*t2 -2.0m/sec*t -6.0m/sec3*t3 .

a) What is its average velocity between 2 seconds and 4 seconds?

b) What is its instantaneous velocity at t=3sec?


To the right is the position vs time graph for two objects. When is the velocity of the objects the same?

QUESTION

xa) (A)

b) (B)

c) (C)

d) (D)

e) (A) and (C)

timeA B DC


Constant Acceleration

constant

a(t) = a


Example Problem 1.2

You are cruising along at 15m/sec, when you pass a police car stopped along the side of the road. 10 meters after you pass the car, you begin to speed up at 2.0m/sec2. How far are you from the police car 5 seconds after you begin to accelerate?

1) Draw a sketch2) Draw a coordinate

system3) What are you looking

for?

Example 1.10 (When does clock start?)

Objects don’t always start to move at

t = 0.


Example:

3 sec after t=0, a cart initially at

rest begins to accelerate at

a=2m/sec2.

What is its position at t=6sec?

Question


3 sec after t=0, a cart initially at rest

begins to accelerate at a=2m/sec2.

What is its position at t=6sec?

a) x = ½*(2)*t2

b) x = ½*(2)*t2 -3

c) x = 3 + ½*(2)*t2

d) x = ½*(2)*(t-3)2

e) x = ½*(2)*(t+3)2

Example 1.11 (2 Carts, 2 Times)


At t=0, blue toy cart starts with a velocity of

10m/sec and an acceleration of -2m/sec2.

4 sec later, a red toy cart starts from the

same position and moves with a constant

velocity of 6m/sec in the same direction.

How long before the blue cart briefly

comes to rest?

How long before the carts collide?

QUESTION

When I ask how long before the carts collide,

algebraically, I’m asking what is t when


a) |xf-blue| is max

b) |xf-red| is max

c) xf-red = xf-blue

d) |xf-red + xf-blue| is max


At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot betweent = 0 sec and t = 1 sec.

How far does it move between t = 1 sec and t = 2 sec?

A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet

Checkpoint 2


the ball is accelerating (gaining speed) while it is rolling down. so that means at t = 1 the ball will be traveling faster than it was at t = 0 therefore it will travel a greater distance in the same amount of time for those two intervals..

B (2 feet)

I used the equation for displacement from motion with constant Acceleration to solve for acceleration using the information from the first second. I found that the acceleration was 2 ft/sec^2. I then put that into the displacement equation using the time and velocity for the interval from 1 to 2 seconds and got 3 feet.

C (3 feet)

The ball is moving 1ft every second, thus it is moving at a velocity of 1ft/sec. The elapsed time between 1 and 2 seconds is 1 second which means that it has only moved 1ft that second

A (1 foot)

Checkpoint 2 Responses

I chose this answer because acceleration is meter*second*second, meaning that the acceleration of the ball is exponential throughout its trip down the ramp with respect to time. From this logic, I found that the ball would have covered 4 feet over the time interval

D (4feet)


1ft4ft

9ft

?

16ft



A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet

QUESTION


1ft4ft

9ft

?

16ft

Graphical View

4m - 1m = 3m




A) 3 feet B) 4 feet C) 7 feet D) 9 feet E) 16 feet

Follow up


1ft4ft

9ft

?

16ft

ACT 5

16m - 9m = 7m

Free fall

Straight forward example of constant

acceleration is “free fall”

If air resistance is negligible, all

objects fall with the same rate of

acceleration

g = 9.81m/sec2


Example Problem 1.4

You drop a small rock from the top of

a 300meter tall building.

What is its velocity after 5

seconds?

What is its position after 5

seconds?


(Note: This is a pretty tall building. The Sears Tower is 527 meters tall.)

Example Problem 1.5

You drop a small rock from the top of


How long does it take to

hit the ground?

What is its velocity just

before it hits?


Example Problem 1.6

You throw a small rock downwards

with a velocity of 20m/sec from the

top of a 300meter tall building.

How long does it take to

hit the ground?

What is its velocity just

before it hits?


Example Problem 1.7

You throw a small rock upwards with

a velocity of 20m/sec from the top of


What is its velocity just before it hits?


Example Problem 1.7

You throw a small rock upwards with

a velocity of 20m/sec from the top of


What is its velocity just before it hits?


How long does it take to hit the

ground?

Example Problem 1.8 (Ball Toss)


A person throws a ball vertically upward into the air with an initial velocity of 15.0 m/s.

➢ How high does the ball go?

➢ How long is the ball in the air before it comes back to the persons hand?

Example 1.9 (Non-constant acceleration)

Can use kinematic concepts with non-

constant acceleration.


Example:

a(t) = 8.0m/sec2 – 0.4m/sec3*t

At t = 0sec, x=0m, v=20m/sec.

What is xf at t=5sec?

Example 1.9 (Non-constant acceleration)

Can use kinematic concepts with non-

constant acceleration.


Example:

a(t) = 8.0m/sec2 – 0.4m/sec3*t

At t = 0sec, x=0m, v=20m/sec.

What is xf at t=5sec?

Motion Diagrams


Imagine you took multiple exposures

every second of an object as it moved.

QUESTION


1 2 3 4 5

1 2 3 4 5

Both cars in the above

motion diagram are

moving in the positive

direction. Which position

graph might represent

the red Car A?

+

A

B

tt

x

(A) (B)

(C) (D)

t

x

t

x

t

x

You are driving your fire-engine red Toyota Prius (with the great CD player) along at 50km/hr(14m/s) when a dog runs out into the road in front of you. It takes you 0.5 second to react and slam on the brakes.

The plot to the right shows your velocity as function of time.

How far will you travel before coming to a stop?

Example 1.12 (Position from velocity)


Method I: Algebraically

Breaking Distance of a Car


A B

Method II: Graphically

Breaking Distance of a Car


Find the area under

the velocity vs time

curve

Integrate!

Question

A car has a negative acceleration of

-4.2m/sec2. We can say magnitude of

the car’s velocity is

A. constant

B. increasing

C. decreasing

D. We can’t really say any of the above


Physics 2111 Unit 1 · 2021. 1. 31. · Physics 2111 Unit 1 Things for Today: Displacement, Velocity, Acceleration –graphically Displacement, velocity, acceleration - numerically

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