Linear Motion 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 = v i t + ½ at 2 v f 2 = v i 2 + 2a  x v f = v i + at x = position, v = velocity, a = acceleration, t = time

Kinematic Equations ∆x = ½ (v i + v f )t If your object starts at x = 0, and v = 0, you can simplify the first equation to ∆x = ½ at 2

Strategies Read the problem – identify the goal – identify given variables 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/s 2 ? An airplane accelerates down a runway at 3.20 m/s 2 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/s 2

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 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?