Exam 0: (trig to free fall/proj mot)

Question 1

how do you calculate sin?

Answer 1

opposite/hypotenuse

Question 2

how do you calculate cos?

Answer 2

adjacent/hypotenuse

Question 3

how do you calculate tan?

Answer 3

opposite/adjacent

Question 4

what determines point sign value?

Answer 4

the placement on the coordinate grid

Question 5

velocity definition?

Answer 5

velocity of particle as a function of time is equal to the derivative with respect to time of the position

Question 6

velocity equation

Answer 6

v(t) = d/dt p(t)

Question 7

what can you do if you know how the position changes over time? (ie the function)

Answer 7

you can take the derivative with respect to time and get the velocity

Question 8

acceleration defintion

Answer 8

acceleration of a particle is equal to the derivative of the velocity (2nd derivative of the position)

Question 9

acceleration equation

Answer 9

a(t) = d/dt v(t)

Question 10

angular velocity definition

Answer 10

angular velocity of a rigid body is the time derivative of the angular position of a rigid body

Question 11

angular position equation

Answer 11

w(t) = d/dt theta(t)

Question 12

angular acceleration definition

Answer 12

angular acceleration of a rigid body is the time derivative of the angular velocity

Question 13

angular acceleration equation

Answer 13

alpha(t) = d/dt w(t)

Question 14

force definition

Answer 14

the force on an object as a function of the position variable is the negative derivative with respect to X of the potential energy

Question 15

force equation

Answer 15

F(x) = -d/dx U(t)

Question 16

You can only take derivatives of ______

Answer 16

functions
- no single point derivatives

Question 17

you always take derivative _____ _____ ____ something

Answer 17

with respect to

Question 18

polynomial derivative equation

Answer 18

d/dx (cx^r) = crx^(r-1)

Question 19

natural log derivative equation

Answer 19

d/dx (c ln(x)) = c/x

Question 20

trig functions with sin and cos derivatives

Answer 20

• d/dx (C cos x) = -CsinX
• d/dx (C sin x) = Ccosx

Question 21

integral definition

Answer 21

the function whose derivative is given function

Question 22

integrals only work for ____ not _____ ____ of variables

Answer 22

functions; single values

Question 23

you should take the integral ___ ___ ___ something

Answer 23

with respect to

Question 24

there is always a ____ __ ___ with integrals

Answer 24

constant of integration

Question 25

how do we calculate constant of integration initial conditions?

Answer 25

given the value of the function when time = 0

Question 26

polynomial integral equation

Answer 26

∫cx^r dx = (cx^(r+1))/r+1 + K

Question 27

natural log integral equation

Answer 27

∫cx^-1 dx = cln(x) + K

Question 28

trig function integrals for cos and sin

Answer 28

- ∫c cos(x) dx = csinx + K - ∫ c sin(x) dx = -ccos(x) + K

Question 29

examples of motion along a line? (6)

Answer 29

- time - position - velocity - acceleration - mass - forces

Question 30

what is the time unit in?

Answer 30

seconds (s)

Question 31

time definition

Answer 31

when you turn the clock on at a relevant instant when stuff is either known or stuff is asked for

Question 32

position properties (3)

Answer 32

1. imaginary number line along a line of motion 2. 0 on the number line at the location of object when t = 0 3. at t, position is the location along the number line when stopwatch says t

Question 33

units for position?

Answer 33

meters (m)

Question 34

velocity properties (2)

Answer 34

1. magnitude is the speed 2. sign is the direction object moves at an instant

Question 35

velocity units?

Answer 35

m/s

Question 36

when is acceleration speeding up? down?

Answer 36

when v and a have the same signs; when v and a have opposite signs

Question 37

contant acceleration

Answer 37

when a(t) = c, c = any number that doesn't change

Question 38

what factors are considered in constant acceleration? (4)

Answer 38

- time - position - velocity - acceleration

Question 39

what are the 3 constant acceleration equations?

Answer 39

1. v = v0 + at 2. p = v0t + 0.5at^2 3. 2ap = v^2 - v0^2

Question 40

what are the 2 requirements for constant acceleration equations?

Answer 40

1. nothing touching 2. air resistance has negligible effect on motion

Question 41

when the 2 constant acceleration conditions are met, what is the downward acceleration?

Answer 41

9.8 m/s^2

Question 42

freefall

Answer 42

an object is always moving down

Question 43

projectile motion

Answer 43

an object is moving up at the start

Question 44

when an object is on the way up: v ___ so a ___

Answer 44

increases; decreases - v slows down towards the high point - overall slowing down

Question 45

when an object is on the way down: v ___ so a ___

Answer 45

decreases; decreases - overall speeding up (same sign)

Question 46

T/F does gravity make heavier things fall faster?

Answer 46

False - only happens because of air resistance

Question 47

when is air resistance significant? (3)

Answer 47

1. weight decreases 2. surface area increases 3. speed increases (largest effect)

Question 48

if an object is dropped, its starting velocity is the same as what?

Answer 48

what its dropped from - for stable objects like building that would be 0

Question 49

if an object is launched up, it reaches its highest point when velocity is ___?

Answer 49

zero

Question 50

end card

Answer 50

:)