Motion in One Dimension

Kinematics Dynamics

Describes motion. The forces that cause motion.

Mechanics

Scalars and Vectors

There are two kinds of measurement: scalars and vectors.

Scalar – has only magnitude (size), such as distance. Ex. 35 m

Vector – has both magnitude and direction, such as position. Ex. 45 km north

Scalars (magnitude

only)Distance

Speed

MassTemperatur

eDensity

Vectors (magnitude

and direction)Displaceme

ntVelocity

Acceleration

Force

Momentum

A jet airplane travelled at 200km/hr towards the southwest. This is an example of a

Vector

Scalar

0%0%

1. Vector2. Scalar

200km/hr to the southwest represents …

Speed

Velocity

Dist

ance

Acceleration

Disp

lacement

0% 0% 0%0%0%

1. Speed2. Velocity3. Distance4. Acceleration5. Displacement

Position

Position (x) – the separation between an object and a reference point.

- it can be positive or negative depending on which side of the reference point that it is

Motion

Anytime an object changes its position (x), it is engaged in motion.

Displacement (Δx) = change in position

. Δx = xf - xi

xf = final position xi = initial position

Distance vs. Displacement

Joe Adams - punt returnDistance (d) = total amount travelled

regardless of direction (the real amount that Adams ran); scalar

Displacement (Δx) = the difference between the final and initial position (the yardage that shows up in the box score); vector

Reference Point

Reference point (or frame of reference) – a point that you label as zero and measure objects distance from

Average Velocity

Average Velocity

Average velocity = change in displacement per unit time

__ v = (xf–xi) / (tf–ti) = Δx/Δt = Δx/t

xf = position at clock reading t2

xi = pos. at earlier clock reading t1

∆x = xf – xi

∆t = t2 – t1

London Olympics and Average Velocity

Pure Speed

Usain Bolt and Average Velocity

In the water ...

Is Usain Bolt’s average velocity in the 200m greater, less, or the same as in the 100m?

Gre

ater in

the 200m

Less

in the 200m

The same in

the 200m (+

..

0% 0%0%

1. Greater in the 200m

2. Less in the 200m

3. The same in the 200m (+/- 1m/s)

Usain Bolt in the 200m

True or False: A car clocked with an average velocity of 85mph east must have been moving faster than a car clocked with an average velocity of 75mph east throughout

the entire time interval.

True

False

0%0%

1. True2. False

It is possible to have a negative velocity.

True

False

0%0%

1. True2. False

Acceleration

Acceleration – a vector quantity that describes the change in velocity over time

a = Δv/t

SI unit = m/s2

Position vs. Time Graphs

Slope = velocity

Straight line (constant slope) = constant velocity

Curved line = changing velocity = acceleration

Velocity-Time Graphs

Area underneath curve or line = displacement

Constant Slope ≠0 : constant acceleration

Zero slope = constant velocity

Acceleration Time Graphs

Used to visually show changes in acceleration.

Area under line = velocity

A velocity time graph with a slope of 0 is definitely not:

Moving

Accelerating

Moving back

war...

All of t

he abo...

0% 0%0%0%

1. Moving2. Accelerating3. Moving

backwards4. All of the above

A position time graph with a slope of 0 is definitely

Moving

Motionless

Accelerating

Moving back

war...

Exploding in

m...

0% 0% 0%0%0%

1. Moving2. Motionless3. Accelerating4. Moving

backwards5. Exploding in

midair

A position time graph that has is curving upward cannot be:

Moving in

the ...

Accelerating

Changing veloc...

At a nega

tive ...

At a co

nstant .

..

0% 0% 0%0%0%

1. Moving in the positive direction

2. Accelerating3. Changing

velocity4. At a negative

position5. At a constant

speed

A position time graph that is linear with a negative slope describes an object which is:

Motionless

Accelerating

Moving at

a co

...

All of t

he abo...

0% 0%0%0%

1. Motionless2. Accelerating3. Moving at a

constant velocity

4. All of the above

A velocity time graph that is linear could possibly describe an object which is:

Motionless

Accelerating

Moving at

a co

...

All of t

he abo...

0% 0%0%0%

1. Motionless2. Accelerating3. Moving at a

constant velocity

4. All of the above

The area between the line and the x-axis on a velocity time graph represents what?

Acceleration

Speed

Disp

lacement

Position

0% 0%0%0%

1. Acceleration2. Speed3. Displacement4. Position

The marble will finish first at the end of which color ramp? (Let the betting begin.)

Red

Gre

en

Yellow

Blue

All the sa

me

0% 0% 0%0%0%

1. Red2. Green 3. Yellow4. Blue5. All the same

The marble will complete the race with the least time on which color ramp?

Red

Gre

en

Yellow

Blue

All the sa

me

0% 0% 0%0%0%

1. Red2. Green 3. Yellow4. Blue5. All the same

Which ramp will the marble have the fastest average velocity? (Place your bets.)

Red

Gre

en

Yellow

Blue

All the sa

me

0% 0%

12%6%

82%1. Red2. Green 3. Yellow4. Blue5. All the same

Which color ramp will the marble have the smallest instantaneous velocity at the end of the ramp? (Place your bets.)

Red

Gre

en

Yellow

Blue

All the sa

me

14% 14%

0%

43%

29%

1. Red2. Green 3. Yellow4. Blue5. All the same

Which color ramp will the marble have the largest instantaneous velocity at the end of the ramp? (Place your bets.)

Red

Gre

en

Yellow

Blue

All the sa

me

0% 0% 0%0%0%

1. Red2. Green 3. Yellow4. Blue5. All the same

Types of Velocity

Constant velocity – this is a situation where the average velocity is the same for all time intervals.

Average velocity – takes into account the entire displacement and time; velocity may not always be constant

Instantaneous velocity – velocity at a given instant

Acceleration

Acceleration – a vector quantity that describes the change in velocity over time

a = Δv/t = (vf – vi)/t

SI unit = m/s2

Acceleration

A rocket ship has a negative acceleration but still seems to be speeding up. Is this possible? Justify your answer with concrete details backed up by data.

Acceleration Matrix

Initial Velocity Acceleration Type of Motion

+ + Speeding up

- - Speeding up

+ - Slowing down

- + Slowing down

+ or - 0 Constant velocity

0 + or - Speeding up from rest

0 0 Remains at rest

A car speeds up from 10 m/s south to 30 m/s south. Describe the acceleration.

Positive

Negative

Zero

Unable to

be d...

0% 0%0%0%

1. Positive2. Negative3. Zero4. Unable to be

determined

A cheetah slows down from 10 m/s south to 5 m/s south. Describe the acceleration.

Positive

Negative

Zero

Unable to

be d...

0% 0%0%0%

1. Positive2. Negative3. Zero4. Unable to be

determined

A minivan slows down from 85 mi/hr to 65 mi/hr when the driver spots a police officer tracking her speed. Describe her acceleration.

Positive

Negative

Zero

Unable to

be d...

0% 0%0%0%

1. Positive2. Negative3. Zero4. Unable to be

determined

An basketball is released from rest. When the ball hits the ground it is moving at a speed of 8m/s. Describe the acceleration.

Positive

Negative

Zero

Unable to

be d...

0% 0%0%0%

1. Positive2. Negative3. Zero4. Unable to be

determined

Tips for Solving Physics Problems

1) List all given information including unknown variable. Look for any inconsistent units (ex. cm and m/s) If all values are in SI units to start with, the final value will be an

SI unit.

2) List formulas that will be used to solve the problem (before plugging in data).

3) Plug in data and solve for unknown.

4) Box your answer and make sure the correct unit is present

EQUATIONS OF MOTION AT CONSTANT

ACCELERATION

Δx t vf vi a