332 Physics - UNIT 1

1-Dimensional Motion

Sign Convention

• A positive value indicates a direction of east, north, right, or up

• A negative value indicates a direction of west, south, left, or down

Motion Terms:

• Distance (d)

• Displacement (Δd)

• Δd = d2 – d1

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:

Example

0 5 m 10 m 15 m

A B C

a) the person’s final positionb) the displacementc) the distance walked.

• Speed (v)

• Average Speed

• Velocity (Δv)

• Average Velocity

• Instantaneous Speed, Velocity

• Constant Speed vs Constant Velocity

• White lines

EXAMPLEYou drive due east from your house to the store 8.75km. It

takes 9.0 minutes and 42s to drive to the store. The car covers the same distance on the way home, but takes 12 minutes and 38s.

a) Determine the average speed for the round trip.

b) Determine average velocity of the car on the return trip?

EXAMPLEUsain Bolt holds the record for the 100m sprint completing it in only 9.58s!

a) Determine his average speed in m/s & mph. (1.6km = 1mile)

b) Mr Sample (I hold no record) ran the Philly half-marathon (13.1mi) in Sept 2009 in 1hr55min36sec. Determine my avg speed in mph.

Graphical Analysis of Motion

Position-time graph:

Describe the position of the objects (A-D) over time. Use origin in your statement.

A

B

t

x

C

D

0

EAST

WEST

What does the intersection of A and B refer to?

Slope of d vs t graph

Recall that slope = Δy / Δx

Slope interpretation – describe slope of lines

Describe the velocity of the objects (A-D) over time. Use origin in your statement.

A

B

t

x

C

D

0

EAST

WEST

Which object had the largest maximum speed at some point?

In which section(s) did the cart have a constant (+) velocity?

In which section(s) did the cart have a constant ( - ) velocity?

Which section had the greatest avg speed?

How fast was the cart moving during BC?

How far did the cart travel in the first 4s?

What was the cart's displacement during these 11s?

Determine avg velocity from D to H

Acceleration

• Definition in words

• Formula

• Units

• Turning

• Can Acceleration be negative?

Example

A car accelerates at 1.5m/s2 to a velocity of +14m/s in a time of 3.5s. Determine the initial velocity.

Constant Acceleration

• Constant acceleration or deceleration implies what about velocity?

• Constant acceleration or deceleration implies what about distance?

• Acceleration of zero implies what about velocity?

Recall: Acceleration tells velocity how to change.

Constant acceleration eqns

Example 1

• A) How far did it travel?

• B) Determine the acceleration.

• C) If after 5.0s it stopped accelerating and coasted, how far would it go in 3.0s?

A large twinkie undergoes a constant acceleration where it reaches a velocity of 8.5m/s in 5.0s after starting from rest.

Example 2

A) If the initial velocity was 2.5m/s, determine the final velocity.

B) Determine the time of the trip.

A car uniformly accelerates at 5.0m/s2 for 100m.

A person who walks two blocks at a moderate speed, waits at an intersection for a short time until the "walk" light turns "green," then walks the next block more

slowly, and finally runs the final two blocks very rapidly

Velocity-time graphs (v vs t)

v

t0

A) Find acceleration from t = 0-2sec

B) Find acceleration from t = 4-8sec

Area under v-t graph

A) Find displacement from t = 0-9sec

B) Did object ever turn around? Explain.

Falling Bodies

Galileo, the incline plane, and Leaning Tower of Pisa

Air resistance, Galileo, the Greeks, and paper & book

FREEFALL• Assume

• Object under control by

Constant acc due to gravity

• Recall what constant acc means?

• In freefall,

• ALL objects undergo

• ALL objects undergo

• Value of acceleration or deceleration

ANATOMY OF FREEFALL

example1

A) How high does it rise?

B) How much time does it take to reach apex?

C) Find velocity at t = 3.0s

D) Determine displacement for whole trip assuming ball returns to launch point.

A ball is launched straight upward with a speed of 25m/s.

Example 2A water balloon is thrown downward at 8.0m/s.

a) How long does it take a water balloon to fall 45m?

b) How fast will the balloon be moving at the 45m mark?

c) Where along the trip does the greatest accelerationof the balloon occur (after it leaves the hand before ithits the ground)?

d) What would a position-time and velocity-time graph look like for the motion of balloon?

Example 3A person stands at the edge of a 70m cliff and throws a ball straight upwards at 12m/s. The ball just misses the cliff on the way down and proceeds to strike the ground down below. Determine the time it takes to reach ground down below.

A student is in a hot air balloon rising at 6.5m/s. She releases a package.

b) How far does package go upward?

c) How far apart are the student and package when the package reaches its peak?

Example 4

a) Describe the motion of package after being released.