Physics unit 1 kinematics describing motion
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PHYSICS UNIT 1: KINEMATICS (Describing Motion). MOTION ALONG A LINE. Who’s Upside Down?. MOTION ALONG A LINE. Who’s Moving?. MOTION ALONG A LINE. Motion : change in position of an object compared to a frame of reference (a "stationary" reference point) Measuring Motion (along a line)

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PHYSICS UNIT 1: KINEMATICS (Describing Motion)

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Physics unit 1 kinematics describing motion

PHYSICS UNIT 1: KINEMATICS (Describing Motion)


Motion along a line

MOTION ALONG A LINE

  • Who’s Upside Down?


Motion along a line1

MOTION ALONG A LINE

  • Who’s Moving?


Motion along a line2

MOTION ALONG A LINE

  • Motion: change in position of an object compared toa frame of reference (a"stationary" reference point)

  • Measuring Motion (along a line)

    • position, x: location with respect to the origin The origin is (x=0), unit: m

    • displacement, s = Dx : change in position

      Dx = xf – xidisplacement = final position – initial position


Motion along a line3

MOTION ALONG A LINE

  • displacement examples


Motion along a line4

MOTION ALONG A LINE

  • time, t: time since motion start, unit: s (text uses Dt)

  • velocity, v: time rate of displacement, unit: m/s

    • average velocity, vav = (xf-xi)/t

    • has same +/- sign as displacement – shows direction of motion along line

    • instantaneous velocity, v: actual velocity at a specific point in time, slope on an x vs. t graph.

      • at constant speed, v=vav

      • for changing speed, vvav


Motion along a line5

MOTION ALONG A LINE

  • Speed: the amount of velocity S=d/t

  • Velocity is speed and direction (+/- along a line), speed doesn’t have direction. V=∆x/t

    • a velocity of -24 m/s is not the same as +24 m/s (opposite directions), but both have the same speed (24 m/s).

    • car speedometer indicates speed only; for velocity, you would need a speedometer and a compass.


Solving problems

SOLVING PROBLEMS

  • Problem-Solving Strategy

    • Given: What information does the problem give me?

    • Question: What is the problem asking for?

    • Equation: What equations or principles can I use to find what’s required?

    • Solve: Figure out the answer.

    • Check: Do the units work out correctly? Does the answer seem reasonable?


Graphing motion

GRAPHING MOTION

  • interpreting an x vs. t (position vs. time) graph

constant +v

constant v = 0

constant –v

changing +v

changing +v

(moving forward)

(slowing down)

(not moving)

(moving backward)

(speeding up)


Graphing motion1

x

t

GRAPHING MOTION

  • interpreting an x vs. t (position vs. time) graph

    • for linear x vs. t graphs:

slope =rise/run =Dx/Dt, so

rise = Dx

slope = vav

run = Dt


Graphing motion2

x

t

GRAPHING MOTION

  • interpreting an x vs. t (position vs. time) graph

    • for curving x vs. t graphs:

slope of tangent line = vinstantaneous


Graphing motion3

GRAPHING MOTION

  • interpreting a v vs. t (velocity vs. time) graph

constant +v

constant v = 0

constant –v

changing +v

changing +v

(slowing down)

(moving backward)

(speeding up)

(not moving)

(moving forward)


Graphing motion4

GRAPHING MOTION

  • comparing an x vs. t and a v vs. t graph


Acceleration

constant velocity

constant acceleration

ACCELERATION


Acceleration1

ACCELERATION

  • Acceleration, a: rate of change of velocity

    • unit: (m/s)/s or m/s2

    • speed increase (+a), speed decrease (–a), change in direction (what are the three accelerators in a car?)

    • average acceleration, aav = (v-u)/t= Dv/t

    • instantaneous acceleration, a: actual acceleration at a specific point in time


Acceleration2

time (s)

0

1

2

3

4

5

6

speed (m/s)

0

2

4

6

8

10

12

position (m)

0

1

4

9

16

25

36

ACCELERATION

  • Constantacceleration (a = aav)

    example: a=2 m/s2

v  t, x  t2


Acceleration3

terms:

t: elapsed time

xf : final position

xo: initial position

s: change in position (xf-xi)

terms:

a: acceleration

vavg: average velocity

vf: final velocity

u, vo: initial velocity

Dv: change in velocity (v-u)

ACCELERATION


Acceleration4

defined equations:

a = Dv/t

vav = Dx/t

vav = (v+u)/2

derived equations:

s = ½(v+u)t

v = u + at

xf = xi + ut + ½at2

v2 = u2 + 2as

ACCELERATION


Graphing motion5

GRAPHING MOTION

  • interpreting a v vs. t (velocity vs. time) graph

For linear v vs. t graphs, slope = a

constant a = 0

constant –a

constant +a

(slowing down)

(speeding up)

(constant speed)


Graphing motion6

GRAPHING MOTION

  • comparing v vs. t and a vs. t graphs


Physics

PHYSICS

UNIT 1: KINEMATICS

(Describing Motion)


Free fall

FREE FALL

  • Free Fall: all falling objects are constantly accelerated due to gravity

    • acceleration due to gravity, g, is the same for all objects

    • use y instead of x, up is positive

    • g = –9.80 m/s2(at sea level; decreases with altitude)


Free fall1

FREE FALL

  • air resistance reduces acceleration to zero over long falls; reach constant, "terminal" velocity.

  • Why does this occur?

  • Air resistance is proportional to v^2


Physics1

PHYSICS

UNIT 1: KINEMATICS

(Describing Motion)


Motion in a plane

Start at the Old Lagoon

Go 50 paces East

Go 25 Paces North

Go 15 paces West

Go 30 paces North

Go 20 paces Southeast

X marks the Spot!

MOTION IN A PLANE


Motion in a plane1

MOTION IN A PLANE

  • Trigonometry

    • sine: sin q = opp/hyp

    • cosine: cos q = adj/hyp

    • tangent: tan q = opp/adj


Motion in a plane2

MOTION IN A PLANE

  • Vectors

    • scalars: only show how much (position, time, speed, mass)

    • vectors: show how much and in what direction

      • displacement, r or x : distance and direction

      • velocity, v : speed and direction

      • acceleration, a: change in speed and direction


Motion in a plane3

q

v

N

E

W

S

MOTION IN A PLANE

  • Vectors

    • arrows:velocity vector v = v (speed), q(direction)

      • length proportional to amount

      • direction in map coordinates

        • between poles, give degreesN of W, degrees S ofW, etc.


Motion in a plane4

MOTION IN A PLANE

puck v relative to earth=puck v relative to table+table v relative to earth


Motion in a plane5

MOTION IN A PLANE

  • Combining Vectors

    • draw a diagram & label the origin/axes!

    • Collinear vectors: v1 v2 v1 v2

      • resultant: vnet=v1+v2 (direction: + or –)

      • ex: A plane flies 40 m/s E into a 10 m/s W headwind. What is the net velocity?

      • ex: A plane flies 40 m/s E with a 10 m/s E tailwind. What is the net velocity?


Motion in a plane6

MOTION IN A PLANE

  • Perpendicular vectors:

resultant’s magnitude:

resultant’s direction:


Physics2

PHYSICS

UNIT 1: KINEMATICS

(Describing Motion)


Unit 1 test preview

UNIT 1 TEST PREVIEW

  • Concepts Covered:

    • motion, position, time

    • speed (average, instantaneous)

    • x vs. t graphs, v vs. t graphs, a vs. t graphs

    • vectors, scalars, displacement, velocity

    • adding collinear & perpendicular vectors

    • acceleration

    • free fall, air resistance


Unit 1 test preview1

UNIT 1 TEST PREVIEW

  • What’s On The Test:

    • 21 multiple choice, 12 problems

      Dx = ½(vf+vi)tvf = vi + at

      xf = xi + vit + ½at2 vf2 = vi2 + 2aDx


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