Introduction to Kinematics Vectors, Scalars, and Motion!

Vector vs. Scalar Quantities Scalar Quantities: –Only has magnitude Vector Quantities: –Have magnitude AND direction –Represented with an arrow –+ or – indicates the direction

Distance vs. Displacement Distance (Scalar) How far you have travelled Displacement (Vector) How far you are from your starting point + or – indicates direction

Let’s Practice! Start 1 meter -1 meter Distance = 1 m Displacement = + 1 m Distance = 3 m Displacement = - 1 m Distance = 2 m Displacement = 0 m Distance = 4 m Displacement = 0 m REMEMBER: “Distance” is how far you have gone “Displacement” is how far you are from the starting point

Speed vs. Velocity Speed (Scalar) How fast an object is moving More precisely, it’s the rate at which an object covers distance Velocity (Vector) The rate at which an object changes its position (displacement!) + or – indicates direction

Average Velocity: the overall displacement covered in a given time period Units = m / s = m·s -1 * Note: average speed = total distance per unit time Instantaneous Velocity: The speed and direction of a moving object at a particular instant in time –Initial velocity  v 1 (or v i or v o ) –Final velocity  v 2 (or v f or v ) More About Velocity

Speed = 2 m ÷ 2 s = 1 m / s Avg. Velocity = 0 m ÷ 2 s = 0 m / s Start 1 metre -1 metre Speed = 1 m ÷ 1 s = 1 m / s Avg. Velocity = + 1 m ÷ 1 s = + 1 m / s Speed = 3 m ÷ 3 s = 1 m / s Avg. Velocity = - 1 m ÷ 3 s = m / s Let’s Practice! REMEMBER: “Speed” is how fast you go “Velocity” is how fast in a given direction Speed = 4 m ÷ 4 s = 1 m / s Avg. Velocity = 0 m ÷ 4 s = 0 m / s

Acceleration (Vector) : ANY change in velocity –Speeding up (final velocity is a larger magnitude than the initial velocity) –Slowing down (final velocity is a smaller magnitude than the initial velocity) –Changing directions (the direction of the vector is changing) Average Acceleration: the rate at which velocity is changing Units = m / s 2 = m·s -2 Acceleration

Speeding up Positive velocity, positive acceleration OR Negative velocity, negative acceleration Speeding up occurs when velocity and acceleration are in the same direction Slowing down Positive velocity, negative acceleration OR Negative velocity, positive acceleration Slowing down occurs when velocity and acceleration are in the opposite direction.

Setting coordinate system Determine which direction is the positive direction and which is the negative direction. –Traditionally, the positive direction is up or right, but as long as you’re consistent within the problem, it is up to you. Determine which quantities in the problem are vectors and draw vector arrows in your diagram representing their relative size and direction

Problem solving strategy –Sketch the problem Establish a coordinate system, determine “0” position Diagram the scenario in the problem, labeling all important known and unknown quantities –What do you know? List all known variables including units –What do you want to know? List any unknown variables—these are what you need to solve for –List the appropriate equation –Plug and chug Insert all known quantities, including units; calculate your answer. –Double check your work

Scalar or Vector? REMEMBER: Scalar quantities have size only and no direction. Vector quantities have both size and direction. ScalarVector 1. Mass 2. Distance 3. Displacement 4. Speed 5. Velocity 6. Energy 8. Power 7. Time 9. Momentum 10. Acceleration 11. Force

Practice Problems Practice Problems (do these in your journal!) 1.Josie jogs around a 400m track around the football field. It takes her 80s to complete a lap a)What is Josie’s distance after 1 lap? Displacement? b)What is her speed after 1 lap? Average velocity? 2.A dog runs +5m to get a ball. He then turns around at runs 2m back to his owner. What distance did he run? What is his displacement? 3.A car travels +20.0m in 2.0s. It then backs up 4.0m in 1.0s. What is the average velocity of the car? Speed? 4.A car accelerates from +8.0 m / s to m / s in 3.0s. Find it’s acceleration. 5.Find the acceleration of a motorcycle that slows down from 18 m / s to 0.0 m / s in 6.0s.