Linear Motion Kinematics Kinematics Kinematics how objects move

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 at 2 • vf 2 = vi 2 + 2 a 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 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( )

2 D 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

2 D 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 2 D 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?