-
Define motion
Motion: change of an object's position or orientation with time. Involves both spatial and temporal change
-
Define Trajectory
Trajectory: path along which an object moves, which might be a straight line or might be curved
-
What are the four types of motion?
- Straight-line | Circular | Projectile | Rotational
-
Illustrate three ways of representing motion
-
Define a Motion Diagram
Motion Diagram: A composite diagram showing an object's positions at several equally spaced instants of time
-
Describe the types of motion displayed
-
Define a Particle Model
Particle model: A simplifying model in which we treat the object as if all its mass were concentrated at a single point. This model helps us concentrate on the overall motion of the object.
-
What does it mean when displacement vectors of a car are lengthening?
-
-
Define Kinematics
Kinematics: Portion of mechanics that describes motion using the concepts of space and time without regard to the causes of motion
-
Kinematics is the description of motion in terms of an object's: (3)
- Position
- Velocity
- Acceleration
-
A particle travels from A to B (dotted line), this is the ______ traveled and is a ______. It depends on the path.
-
-
Displacement always points from the object's initial position to its ______ position, regardless of the path the object took. Magnitude is the shortest distance between the _____ and ______ positions
- final positions
- initial and final positions
-
Define Elapsed time
What is the equation for Δt and what is its sign?
- Elapsed time (Δt): the duration of time as an object moves from an initial position xi at time ti to a final position xf at time tf.
- Δt = tf - ti
- Δt is always positive as tf which is always a later time than ti
-
Velocity tells us how fast an object's _______ changes. Velocity is a _____, it always points in the same direction as ______
- position
- vector
- displacement
-
What should a person in motion do if they wish to maximize their velocity?
They should never change directions and begin to return to the starting position
-
What information must be included in order to fully describe the velocity of an object?
- Direction
- E.g. an object's velocity as being 55 mi/h, east
-
What is one formula for average velocity?
-
What can be said of the speeds and velocities of both bikes being represented?
Both bikes are traveling at the same speed, but with different velocities as they travel at different directions
-
A is moving faster because the arrows between the dots are longer
-
State what information each of these tells you
Odometer:
Speedometer:
Pressing the gas pedal:
Pressing brake:
- Odometer: measure distance
- Speedometer: measure speed
- Gas pedal: speeding up/acceleration
- brake pedal: slowing down/deceleration
-
-
-
Define speed
Speed: a scalar quantity that tells the distance traveled per time | the rate at which an object covers distance | How fast an object is moving
-
A fast-moving object has a high speed covers a relatively ______ distance in a ______ amount of time. A slow moving object that has a low speed covers a relatively _______ amount of distance in the same amount of time. An object with no movement has ____ speed
-
Average speed formula:
is it a positive or negative value?
- average speed vavg = (total distance traveled in a given time interval)/time interval
- ALWAYS POSITIVE
-
- 1) They are the same
- 2) The numbers are the same but have opposite signs (not just that one is negative, but to show they go in opposite directions)
- 3) Total distance is will be larger than displacement
-
- A) Total distance = 2d
- T (A->B) = d/5
- T (B->A) = d/3
- Total time = TA->B + TB->A = d/5 + d/3 = d(8/15)
- avg speed = total distance/total speed = 2d/(8d/15) = 3.75 m/s
- B) Its zero because its (a distance - itself) divided by a change in time = 0/Δt = 0
-
State the general equation for instantaneous velocity
What type of value can it be? (Can it a negative value?)
What does the triple line mean?
- triple means it is an identity
-
Instantaneous speed (define)
What type of value can speed be?
- Instantaneous speed: magnitude of the instantaneous velocity vector
- Speed can only be positive never negative
-
Define acceleration
State the equation for average acceleration
- Acceleration: a measure of how rapidly the velocity is changing
-
What happens in each scenario
What are the dimensions and expected units for acceleration?
- speed up | acceleration
- slow down | deceleration
- vector quantity
- [a] = L/T2
- SI units = m/s2
-
State the slope and quadrant of each scenario described
-
Instantaneous acceleration is the limit of the average acceleration as ____ approaches 0. What is the formula for Instantaneous acceleration?
vx = ?
What is another way of representing the formula for ax as it pertains to vx
- Δt
-
Various changes in a particle's motion may produce an acceleration. Name three possible ways to generate an acceleration
- The magnitude of the velocity vection (i.e. speed) may change
- The direction of the velocity vector may change, even if the speed remains constant
- Both may change simultaneously
-
What are two possible scenarios in which the acceleration can be zero
- When A is zero:
- You can be static (not moving)
- You might be moving at a constant velocity
-
What are three possible scenarios in which the direction of the velocity vector may change, even if the speed remains constant
- If V is changing you have 3 options
- 1) speeding up or slowing down
- 2) changing direction
- 3) changing speed and direction
-
-
What are the three types of graphing representation for motion
- Position vs Time
- Velocity vs Time
- Acceleration vs Time
-
The slope of a position vs time graph gives the _________.
Within this context explain average velocity and instantaneous velocity
- velocity
-
The instantaneous velocity can be ______, _______ or _______. Steeper slopes corresponds to ______ speeds. The direction of the instantaneous velocity vector at any point in a particle's path is along a line ________ to the path at that point in the direction of motion
-
- positive, negative or zero
- faster
- tangent
-
The slope of a velocity vs time graph gives the ________. The area under a velocity vs time graph gives the _________.
The area from A to B gives ______ area
The area from B to F gives ______ area
- acceleration
- displacement
- positive
- negative
-
The area under an acceleration vs time graph gives the change in ________.
change in velocity
-
State the slope and area under the curve for each scenario
x vs t = position vs time
Area > 0 if area _____ time axis
Area < 0 if area _____ time axis
- above
- below
-
- A and C are worst options
- B & D are best option
- D is the right answer
-
-
Uniform motion means acceleration = _____
zero
-
Define Straight line motion
Straight line motion aka uniform or constant velocity motion: equal displacements occur during any successive equal time intervals
-
Draw three graphs that represent motion at constant velocity
-
If the velocity of a particle is constant, its instantaneous velocity at any instant is the same as the _____ _____ over given time period. State as equation
Also, what if ti = 0 and tf = t
- average velocity
-
If the acceleration of a particle is constant
ax = ?
Taking ti = 0 and tf = t:
vxf =
Average velocity (2nd equation):
vx,avg =
- ax = Δvx/Δt = (vxf - vxi)/tf - tiVxf = vxi + axtvx,avg = 1/2(vf +vi)
-
State the 4 kinematic equations for motion of a particle under constant acceleration
Kinematic motion is along the ___ axis. At t = 0, the position of the particle is ___ and its velocity is ___
*Hint:
Velocity as a function of time
Position as a function of velocity and time
Position as a function of time
Velocity as a function of position
-
- x-axis
- xi
- vxi
-
Problem solving strategy: Particle Under Constant Acceleration
-
- vi = 12 cm/s
- xi = 3 cm
- ti = 0 s
- tf = 2 s
- xf = -5 cm
- xf = xi + vit + 1/2at2
- a = 2/t2(xf - xi - vit)
- 2/22(-5 - 3 - 12(2)) cm/s2
- -16 cm/s2
-
Notice accelerations are the same
- vxf2 = vxi2 + 2ax(xf - xi)
- 352 = 02 + 2ax(40-0)
- 1225 = 80ax
- ax = 15.3125 mi/h2vxf2 = vxi2 + 2ax(xf - xi)
- 702 = 02 + 2ax(x)
- 4900 = 2(15.3125)(x)
- 4900 = 30.625x
- x = 160 ft
-
1. Free-falling object: We use the coordinate ____. Positive values of it extend ______
2. Motion on a ramp: For motion along a straight slope, we use the coordinate ____. Positive values of it extend to the ______
- y
- upward
- x
- right
-
Define: A freely falling object
Freely falling object: is any object moving freely under the influence of gravity alone (neglecting air resistance)
-
All objects fall with the same acceleration near Earth's surface, a = g = ________ vertically downward
9.80 m/s2
-
What are the three conditions that result in a freely falling object
- Dropped (released from rest)
- Thrown downward
- Thrown upward
-
For an object dropped from rest, the velocity vectors point ______ and get ______. The acceleration points ______
The graph has a _______ slope thus the free-fall acceleration is _______
If the object is initially moving up, the velocity vectors point _____ and get _______. Then the acceleration points ______
- downward
- longer
- down
- constant slope
- constant
- upward
- shorter
- down
-
D. Acceleration is always negative so the slope will be negative and it should be constant which rules out B and C
-
- yi = 0
- yf = 4.00 m
- ti = 0 s
- tf = 1.5 s
- vi = ?
- yf = yi + vyit + 1/2(ay)(t2)
- 4 = 0 + vyi(1.5) + 1/2(-9.8)(1.52)
- 4 = 1.5vyi - 11.025
- 15.025 = 1.5vyi
- vyi = 10.01667 m/s
- vyf = vyi + ayt
- vyf = 10.01667 + (-9.8)(1.5)
- vyf = -4.7 m/s
-
Explain the labels
The crate accelerates due to the action of _______, but it is constrained to accelerate _______ to the surface: a x = _______
What will the correct sign depend on?
-
- gravity
- parallel
- ax = ±gsinθ
- The correct sign depends on which direction the ramp is tilted. As it is here it will be +gsinθ
-
- ax = g(sinθ)
- ax = 9.8(sin(21°))
- ax = 3.5 m/s2
- vxf2 = vxi2 + 2ax(xf - xi)
- vxf2 = 0 + 2(3.5)(120)
- vxf2 = 840
- vxf = 29 m/s
-
Motion in two dimensions can be modeled as two _________ motions in the x and y directions.
Any influence in the y directions does not affect the _______ in the x direction and vise versa
Resolve all vectors into their components:
- independent
- motion
-
Pg 56 -57 for more detailed Problem solving strategy
-
-
An object moves through the air in both x and y directions simultaneously under the influence of _______ and nothing else. The path of motion is a ________ graph.
What two assumptions make this possible
- gravity
- parabola
- 1) Vertical motion: treat as free-fall motion with acceleration ay = g = 9.80m/s2, constant over the range of motion and directed downward
- 2) The effect of air resistance is negligible, thus we can assume no horizontal acceleration, ax = 0
-
The horizontal and vertical components of the motion are ________. The horizontal motion is _______; the vertical motion is _____ _____
- independent
- constant
- free fall
-
Label the diagram
-
State the formula for maximum height, h, and the formula for horizontal range,R
-
Where does the maximum range occur?
Complementary angles will produce the same _______.
The maximum _______ and the ______ of the flight will be different for the two angles
- θi = 45°
- range
- height and the time
-
|
|
