Unit 2 Class Notes

Honors Physics

The Kinematics Equations (1D Equations of Motion)

Day 1

Introduction to the 1D equations of motion

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Δx = x2 − x1

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v = ΔxΔt

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a = ΔvΔt

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Δv = v2 − v1

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s = d Δt

Δx 12 at

2 v1t

v22 v1

2 2aΔx

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v2 = v1 + at

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Δx = 12 t(v1 + v2)

ACCELERATION

Leonardo

Δx 12 at

2 v1t

Michaelangelo

v22 v1

2 2aΔx

v22

Raphael

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v2 = v1 + at

Donatello

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Δx = 12 t(v1 + v2)

Derivations of the equations (a.k.a. where the turtles come from)

Raphael …. slope of the line =

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a =(v2 − v1)

Δt

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v2 = v1 + at

Donatello

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Δx

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Δx = 12 Δt(v1 + v2)

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area = 12 h(b1 +b2)

…. area under curve =

What about Leonardo and Michelangelo?

Fighting with the turtles

List what you have (using “COMPATIBLE” units & using proper SIGNS)

Choose your warrior (in other words, “choose your equation”)

Solve the equation

Make sure your answer makes sense (both in MAGNITUDE & DIRECTION)

Make a decision as to which direction is POSITIVE & which is NEGATIVE

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v1 =100 kmh = 27.7 m

s

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v2 = 0

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t = 4.5sec

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v2 = v1 + at

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0 = 27.7777777 + a(4.5)

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a = −6.17 ms2

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Δx = 12 t(v1 + v2)

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Δx = 12 (4.5)(27.77777 + 0)

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Δx = 62.5m

2.

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v1 = 8 ms

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a = 2 ms2

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Δx =100m

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Δx = 12 at

2 + v1t

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100 = 12 (2)t 2 + 8t

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0 = t 2 + 8t −100

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t = −14.77sec, 6.77sec

3.

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v1 = 40 ms

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v2 = 20 ms

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Δx = 50m

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v22 = v1

2 + 2aΔx

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Δx = 12 t(v1 + v2)

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50 = 12 t(40 + 20)

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t =1.67sec

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202 = 402 + 2a(50)

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a = −12 ms2

4.

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v1 = 0 ms

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v2 = 60mph = 26.82 ms

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t = 3.5sec

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v2 = v1 + at

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26.82 = 0 + a(3.5)

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a = 7.66 ms2

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Δx0−1 = 12 at

2 + v1t

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=12 (7.66)(1)2 + 0(1)

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=3.83m

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Δx0−2 = 12 at

2 + v1t

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=12 (7.66)(2)2 + 0(2)

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=15.32m

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d0−1 = 3.83m d1−2 =15.32m − 3.83m =11.49m

5.

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v22 = v1

2 + 2aΔx

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v1 = v

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v2 = 0

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Δx = x€

02 = v 2 + 2ax

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a = −v 2

2x

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v22 = v1

2 + 2aΔx

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02 = (2v)2 + 2−v 2

2x

⎛

⎝ ⎜

⎞

⎠ ⎟Δx

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v1 = 2v

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v2 = 0

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Δx = ?

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a = −v 2

2x

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0 = 4v 2 −v 2

xΔx

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4v 2 =v 2

xΔx

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Δx = 4x

6.

1 2 3

1-2 2-3 1-3

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v1 = 0

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Δx23 = 20m

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t23 =1.40sec

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a = 3 ms2

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a = 3 ms2

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v1 = 0

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a = 3 ms2

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v2 =12.186 ms

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v3 =16.386 ms

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v2 =12.186 ms

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Δx = 24.75m

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t = 5.462sec

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v3 =16.386 ms

The 5th ninja?

Chris Farley

d rt

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Δx = 12 at

2 + v1t

TONIGHTS HWComplete pp. 61-62, #’s 61-69 (skip 62 & 66), 71, 72