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Describing Motion Kinematics in One Dimension

Sign Convention Direction

Distance Displacement

Distance (x) equates

Displacement equates to

Displacement

Displacement is written

Example

- A person moves on the number line shown below.

The person begins at B, walks to C, and then

turns around and walks to A. For this entire

range of motion DETERMINE - the persons final position
- the displacement
- the distance.

Speed Velocity

Speed How far

Velocity How

Average Speed Velocity

Example

A commuter drives 15.0km on the highway at a

speed of 25.0m/s, parks at work and walks 150m at

a speed of 1.50m/s from his car to his office.

(a) Determine the total time of the commute.

b) Determine the average speed of the entire

commute

EXAMPLE

Usain Bolt holds the record for the 100m sprint

completing it in only 9.58s!

a) Determine his average speed in m/s. (1.6km

1mi)

Did he run faster than this at some point?

b) Mr Sample (I hold no record) ran the Philly

half-marathon (13.1mi) in 1hr55min36sec.

Determine my avg speed in mph.

Example A woman starts at the entrance to a

mall and walks inside for 185m north for

10minutes. She then walks 59m south in 3minutes

to another store. She then leaves the store and

moves south 155m in 8minutes to reach her car

outside.

Determine her average velocity during the trip.

Instantaneous Velocity

The instantaneous speed or velocity is how fast

an object is moving at a single point in time.

Does the gauge on your dashboard give you speed

or velocity?

Does this gauge give you an average or

instantaneous value?

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Acceleration

Acceleration is

Units?

Constant Acceleration

- Constant acceleration implies what about

velocity? - Constant acceleration or deceleration implies

what about distance? - Acceleration of zero implies what about the

velocity?

Negative acceleration vs Positive acceleration

Both can equate to slowing down. When sign of

acceleration matches sign of velocity, object

speeds up in direction of that sign. When signs

oppose, object slows down in direction of v.

Graphical Analysis of Motion

Position-time graph

Describes the position of object during a given

time period.

Describe the position of the objects (A-D) over

time. Use origin in your statement.

x

A

E A S T

B

What does the intersection of A and B refer to?

0

t

WE S T

C

D

Slope of x vs t graph

Recall that slope ?y / ?x

Slope Interpretation

Describe the velocity of the objects (A-D) over

time.

x

A

E A S T

B

0

t

WE S T

C

D

What was the total distance traveled?

Example

What was the displacement for the entire trip?

What was the average speed for the first 6 sec?

What was the velocity of the object btw 2-4 sec?

What was the average velocity from B to E?

In which section(s) was there a constant

velocity?

In which section(s) was there a constant negative

velocity?

In which section had the maximum speed?

Instantaneous velocity

Unlike vavg, instantaneous velocity occurs at a

single point. How would we find vinst at t

3.0s?

At what time(s) does the cart have a zero

velocity?

Describe the velocity btw 0.0 - 0.80s?

Describe the velocity btw 2.6 - 3.2s?

a) During what time periods, if any, is the

object's velocity constant?

b) At what time is its velocity the greatest?

c) At what time, if any, is the velocity zero?

d) Does the object run in one direction or in

both along its tunnel during the time shown?

Graphical Analysis of Motion (2)

velocity-time graph

Describes the velocity of object during a given

time period.

Describe the velocity of each object during its

motion, including initial velocity

V E L O C I T Y

A

B

time

C

D

Crossing t-axis ?

Intersection of lines on vt graph means ?

Slope of v vs t graph

Example

a) Determine the time(s) where object had -

acceleration

b) Determine the time(s) where object had

positive non-zero velocity

c) Determine the time(s) where object was at rest

d) Determine the time(s) where object had

constant velocity.

Example

Determine acceleration of object between 4-9s

At what time(s) did object turn around?

During what time period(s) did object slow down?

When did object reach maximum speed?

When did object possess maximum acceleration?

Instantaneous acceleration

Instantaneous acceleration occurs at a single

point. To find ainst at t 0.6s

Constant Acceleration Eqns

We can write avg velocity 2 different ways

Combining the two eqns yields

Constant / Uniform Acceleration Equations

EXAMPLE

While driving along at 20m/s, you notice the

light up ahead turns red (110m away). Assuming

you have a reaction time of 0.5s,

a) How far from the light are you when you begin

to apply the brakes?

b) What constant acceleration will bring you to

rest at the light?

EXAMPLE 2

A car starts from rest at a stop sign. It

accelerates uniformly at 4.0m/s2 for 6.0s, coasts

for 2.0s, and then slows down at 3.0m/s2 for the

next stop sign.

a) How far apart are the stop signs?

b) Determine the maximum velocity during the trip.

v-t graphs part 2

v-t graphs part 2

Determine the displacement of the object from

20s-38s.

a vs t graph

a

0

t

We will only deal with constant accelerations.

Reference Frames Relative Motion

Any measurement of position, distance, or speed

must be made

In order to determine the speed of object moving

in a particular RF, we use subscripts

VBG6m/s

VSG 20m/s

How fast is bike moving relative to bus?

VSG 20m/s

VCG -30m/s

How fast is bus moving relative to car?

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Falling Acceleration

FREEFALL

Anatomy of a upwardly thrown object

EXAMPLE 1

A ball is thrown upward with an initial speed of

15.0m/s Assume negligible air resistance.

a) Find the maximum height attained by the ball.

b) How much time does it take to reach the apex?

c) Determine the velocity 2.2s into flight.

EXAMPLE 2

As a part of a movie stunt a stunt man hangs from

the bottom of an elevator that is rising at a

steady rate of 1.10m/s. The man lets go of the

elevator and freefalls for 1.50s before being

caught by the end of a rope that is attached to

the bottom of the elevator.

(a) Calculate the velocity of the man at the

instant he is caught by the rope.

(b) How long is the rope?

EXAMPLE 3

An honors physics student stands at the edge of a

cliff that is 36m high. He throws a water

balloon straight up at 12.5m/s so that it just

misses the edge of the cliff on the way down.

Determine velocity of balloon as it strikes

ground below (many ways to solve)

Collaborate with person next to you to answer

following questions

Three students are standing side-by-side next to

the railing on a fifth floor balcony.

Simultaneously, the three students release their

pennies. One student drops a penny to the ground

below. The second student tosses penny straight

downwards at 15 m/s while third student tosses

penny straight upwards at 15 m/s. Assume

freefall.

a) Which penny or pennies strike(s) ground first?

b) Which penny or pennies strike(s) ground last?

c) Which penny or pennies strike(s) the ground

with the greatest final velocity?

d) Which penny or pennies strike(s) the ground

with the greatest acceleration?