1-D Kinematics B

8/2/2019 1-D Kinematics B

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1-D Kinematics

PART 1


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Restrictions

All motion is along a straight line only.

We dont care WHY an object moves.

In kinematics, we will only examineHOW it moves.

The moving object is considered to

move like a particle (no rolling).


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Magnitude & Scalars

The magnitude of a measurement isits size

Ex: the number of miles betweenSocorro and Albuquerque is amagnitude

A scalar is a quantity that has onlymagnitude


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Vectors

A vector has both magnitude & direction

Ex: the displacement vector from Socorro toAlbuquerque is 70 miles long and points duenorth

Vectors are equal if and only if they have thesame magnitude and the same direction

Ex: the displacement vector from Socorro toAlbuquerque is not equal to the displacementvector from Albuquerque to Socorro becausethe direction of the vectors is different


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Distance vs. Displacement

Distance is a scalarquantity (it hasmagnitude only).

Displacement is a vectorquantityand is always relative to the origin.


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Stand in one of tiles on the floor(leave a good amount of room

between you and your neighbor.) This is your origin. Determine +/-

directions.

Move 3 tiles to the right.

Move 2 tiles forward.

Move 5 tiles to the left.

Move 2 tiles backward.


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What is your displacement?

What is the total distance youtraveled?

Displacement is notedx.x = x x0


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Scalar or Vector?

The acceleration of a plane as ittakes off?

The number of passengers on theplane

The duration of the flight The displacement of the flight The amount of fuel required for

the flight

The odometer reading in your car The speedometer reading in your

car

Vector Scalar

Vector ScalarVector Scalar

Vector Scalar

Vector ScalarVector Scalar

Vector Scalar


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Speed vs. Velocity

Average Speed

(scalar)

Distance Traveled

Total time

t

xv

Average Velocity(vector)

DisplacementTotal time

t

xv

Velocityhas a

direction!!


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Try it

Calculate the average speed andaverage velocity of a complete round-

trip in which the outgoing 200 km iscovered at 90 km/h, followed by aone-hour lunch break, and the return200 km is covered at 50 km/h.

Average speed = 60 km/h

Average velocity = 0


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Acceleration

AverageAcceleration

(vector)

VelocityTotal time

t

va

Acceleration is the rateof change of velocity.

Units: m/s2


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The Kinematics Equations

The Kinematics equations are based on two veryimportant assumptions:

1. Constant acceleration. Many situations exhibit

uniform (constant) acceleration. Since accelerationis constant, the average and instantaneousacceleration are equal:

2. t0 = 0. Since we can create our own referencesystem, we might as well make it an easy one.

aa


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Kinematics Equations

atvv 0

2

0vv

v

2

00

2

1attvxx

xavv 22

0

2No time


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Try it

A car slows down from 25 m/s to restin a distance of 85 m. What was its

acceleration, assumed constant?

a = -3.7 m/s2


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Try some more

1. A light plane must reach a speed of 30.0m/s for takeoff. How long a runway isneeded if the acceleration is 3.0 m/s2?

2. A car traveling at 45 km/h slows down at aconstant 0.50 m/s2just by letting up on thegas. Calculate (a) the distance the carcoasts before it stops, (b) the time it takesto stop, and (c) the distance it travelsduring the first and fifth seconds.

x = 1.5 x 102 m

(a) 160 m (b) 25 s (c) 12 m, 10 m


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Falling Objects

When gravity acts on an object, whathappens?

The object falls

We call this free fall

An object is in free fall when it is affectedonly by gravity

astronauts


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Falling Objects

Conveniently, you can use the same kinematicsequations with falling objects (your system is justvertical instead of horizontal).

Replace position x with position y

Is the acceleration in vertical motion constant orchanging?

g = 9.81 m/s2


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Kinematics Equations

atvv 0

2

00 2

1

attvxx

yxavv 22

0

2No time

gtvv 0

2

00 2

1

gttvyy

ygvv 22

0

2

Horizontal Motion Vertical Motion


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Gravity

What is the direction of gravity?Toward the center of the planet.

What is the sign (+/-) of gravity?

The sign of g is often debated. The key is toalways draw a picture, label your coordinatesystem and stick with it.

If you call up the positive (+y) direction,what sign does gravity have?

What if you decide down is positive?


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Questions

1. Will a Nerf ball and a softball fall atthe same rate?

2. How about a feather and a rock?3. Are acceleration and velocity always

in the same direction?

4. If you throw an object up in the air

and catch it again, what is thevelocity at the top of its arc? What isits acceleration?


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King Kong

Exhausted by hours of batting away planes, King

Kong topples off the Empire State Building.Calculate (a) how long it will take the big ape to

reach the ground (assume a straight path,h = 380 m), and (b) his velocity just beforelanding.

1. Draw a picture.

2. Label coordinates (axis)3. List known variables

4. Determine what youre looking for

(a) t = 8.8 s (b) v = 86 m/s

Do we need to know King Kongs weight?


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More Good Stuff

1. A stone is dropped from the top of a cliff. Itis seen to hit the ground below after 3.50 s.How high is the cliff?

2. A stone is thrown vertically upward with aspeed of 20.0 m/s. (a) How fast is it movingwhen it reaches a height of 12 m? (b) Howlong is required to reach this height? (c)Why are there two answers to (b)?

y = 60.1 m

(a) v = 13 m/s (b) t = 0.73 s, 3.3 s

(c) the motion follows a parabolic path

1-D Kinematics B

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