Linear Motion
Kinematics
Kinematics
• Kinematics – how objects move
• Dynamics – why objects move
Types of Motion
• Translational Motion
– All parts move the same
• Rotational Motion
– The parts rotate or revolve
Types of Motion
• 1 Dimensional
• 2 Dimensional
Types of Motion
• No acceleration
– Paper falling
• Constant acceleration
– Ball falling
• Non-constant acceleration
– Feather falling with wind blowing
Distance, Velocity, &
Acceleration
• Distance vs. Displacement
– Distance – total length traveled
– Displacement – length between start and end
points
• Speed vs. Velocity
– Speed = distance ÷ time
– Velocity = speed with a direction
• Acceleration = velocity ÷ time
Vectors and Scalars
• Scalars have a number and a unit
– Mass, time, length, speed
• Vectors have a number, a unit and a direction
– Displacement, velocity, acceleration
Velocity
• has a magnitude (#) and direction
• For objects experiencing no acceleration
v = distance / time
Acceleration
• Acceleration is a change in velocity
– change in magnitude AND/OR
– change in direction
• a = velocity / time
Motion Graphs
• No acceleration
• Constant acceleration
Motion Graphs
• Car Lab
Motion Graphs
• No acceleration
– position graph is sloped line
– velocity graph is horizontal line
– acceleration graph is horizontal line at a=0
Motion Graphs
• Constant acceleration
– position graph is a parabola
– velocity graph is sloped line
– acceleration graph is horizontal line
Kinematic Equations
• Equations of motion for objects with constant
acceleration
• x = vit + ½ at2
• vf2 = vi2 + 2ax
• vf = vi + at
x = position, v = velocity, a = acceleration, t = time
Kinematic Equations
• ∆x = ½ (vi + vf)t
• If your object starts at x = 0, and v = 0, you can
simplify the first equation to
∆x = ½ at2
Strategies
• Read the problem
– identify the goal
– identify given variables
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Identify the correct equation
Substitute
Do the math
Check for reasonableness
Include units
Examples
• How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if
it accelerates from rest at a constant 2.00
m/s2?
• An airplane accelerates down a runway at 3.20
m/s2 for 32.8 s until is finally lifts off the
ground. Determine the distance traveled
before takeoff.
Free Fall
• An object in free fall is any object in which the
only force acting on it is gravity.
• The acceleration due to gravity close to the
surface of the earth is 9.8 m/s2
Acceleration on an Incline
• When an object is moving down an incline the
acceleration the object experiences is equal to
gsin()

2D Motion
• must be broken into x and y components
• use SOH CAH TOA or Pythagorean Theorem
• once broken into components, do not use
combined numbers again
• apply kinematic equations for each direction
2D Motion
• An airplane flies horizontally at 300 m/s.
When it is 10,000 m in the air, it drops a
package. The package falls to the ground.
– How long does it take for the package to hit the
ground?
– How far horizontally does the package travel in
this time?
Projectile Motion
• Common form of 2D Motion
• An object is given an initial velocity
• Once the object is in motion, the only force
acting on the object is gravity
• Moves in a parabolic path
Projectile Motion
• A rocket is launched at an angle of 450. Its
initial velocity is 50 m/s.
– How high does the rocket travel?
– How long is the rocket in the air?
– How far does the rocket travel horizontally?