physics 2111 unit 1 - college of dupage...mechanics lecture 1, slide 20 example problem 1.2 you are...

Physics 2111

Unit 1

Outline for this unit: Displacement, Velocity, Acceleration – graphically

Displacement, velocity, acceleration - numerically

1-D Kinematics with constant acceleration

Free-fall

Mechanics Lecture 1, Slide 1


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



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


Which pair of these graphs could represent the same motion?

QUESTION

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


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

QUESTION

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


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?

QUESTION

+

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



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?

QUESTION

+

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 left.

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?


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?


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


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 = 3 sec and t = 4 sec?

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

Follow up

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?


Question

You throw a small rock upwards with a velocity of

20m/sec from the top of a 300meter tall building.



We’re going to try to solve this

problem using the formula

vf2 = vi

2 + 2aDx.

What is Dx in this case?

a) 300m

b) less than 300m

c) more than 300m

Question

You throw a small rock upwards with a velocity of

20m/sec from the top of a 300meter tall building.



We previously calculated the final velocity

of the rock when we threw is downwards at

20m/sec as 79m/sec. How will that

compare to our final velocity now that we’re

throwing it upward?

a) vf > 79m/sec

b) vf = 79m/sec

c) vf < 79m/sec

Example Problem 1.7

You throw a small rock upwards with

a velocity of 20m/sec from the top of




How long does it take to hit the

ground?

I throw a tennis ball straight up into the air and then catch it in my hand at the same level from which I threw it.

Which of these plots could represent the velocity of the ball during the entire time of its flight?

QUESTION

v v

v v

(A) (B)

(C) (D)


The plot to the right shows velocity vs time for a tennis ball thrown into the air.

At what point is the ball at its highest position?

QUESTION

vtime

A

B

C


a) The velocity is zero, the acceleration is positiveb) The velocity is zero, the acceleration is zeroc) The velocity is zero, the acceleration is negatived) The velocity is zero, but we can’t tell the

acceleration from this plot

QUESTION

vtime

A

B

C


The plot to the right shows velocity vs time for a tennis ball thrown into the air.

At point B:

Question


You drop a rock from a bridge to the river. When the rock has fallen 4meters, you drop a second rock. As the rocks continue their free fall, the distance between them will

a) remain constantb) increasec) decreased) We can’t really say any of the above

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?

a) What does DX equal so that vf has its maximum positive value.

b) What does DX equal so that vf is zeroc) What does DX equal so that vf has its

maximum negative value

QUESTION


When I ask how high the ball goes, that means that algebraically, we’re going to calculate

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?

QUESTION


To find the position at t=5sec for an

object with the acceleration of:

a(t) = 8.0m/sec2 – 0.4m/sec3*t

we’re going to:

a) have to do an integral

b) use xf = x0 + v0t + 1/2at2

c) use vf2 = v0

2 + 2aDx

d) it can’t be calculated

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

QUESTION


Both cars in the above

motion diagram are

moving in the positive

direction. At what time

do two cars have the

same velocity?

A)Between times 3 and 4

B)Between times 1 and 2

C)time 2

D)time 5

E) times 2 and 5

1 2 3 4 5

1 2 3 4 5

+

A

B


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

Remember this one??

xa) (A)

b) (B)

c) (C)

d) (D)

e) (A) and (C)

timeA B DC

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 - college of dupage...mechanics lecture 1, slide 20 example problem 1.2 you are...

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