KINEMATICS and MOTION Kinematics is the description of how objects move. Motion is a change in position relative to a frame of reference. A frame of reference is a point or object from which motion is determined. o A frame of reference is assumed to be fixed. o The surface of the Earth is the most common frame of reference used by humans to determine motion.

Before describing motion, you must set up a coordinate system – define an origin and a positive direction. Positive direction Negative direction

Displacement Displacement (x or y) "Change in position" It is not necessarily the total distance traveled. In fact, displacement and distance are entirely different concepts. Displacement is relative to an axis. o "x" displacement means you are moving horizontally either right or left. o "y" displacement means you are moving vertically either up or down. o The word change is expressed using the Greek letter DELTA ( Δ ). o To find the change you ALWAYS subtract your FINAL - INITIAL position o It is therefore expressed as either Δs = s f - s i or Δx = x f - x i or Δy = y f - y i Distance - How far you travel regardless of direction.

Distance is the total length of travel.

Displacement is the change in position.

The blue line shows the The red line shows the A student walks along the blue (curved) path shown below from point P to point Q.

Example Suppose a student walks from the lockers (at a position x = 1.0 m) to the physics lab (at a position x = 9.0 m), as shown below.

Example If the woman leaving the physics lab (at x = 9.0 m) walks to where the man started (at x = 1.0 m), what is her displacement?

Example Suppose the student walks from the lockers to the physics lab, turns around, And walks back to where he started. What is the DISPLACEMENT for the entire trip? What is the total DISTANCE for the entire trip?

Speed SPEED is simply the “RATE at which DISTANCE changes”. A rate is any quantity divided by time. speed = distance/time There are three (3) types of speed:

Velocity Velocity is defined as: “The RATE at which DISPLACEMENT changes”. Average SPEED is simply the “RATE at which DISTANCE changes”.

Q: What information is given by the speedometer of car? A) Constant Speed B) Average Speed C) Instantaneous Speed D) All of the Above Q: Speed limit signs tell drivers the maximum _____ they can legally drive. A) constant speed B) average speed C) instantaneous speed D) All of the Above

Average velocity = displacement / elapsed time

During a 3.00 s time interval, the runner’s position changes from 50.0 m to 30.5 m as shown in the figure. What was the runner’s average velocity?

EXAMPLE #2 How far in kilometers can a cyclist travel in 2.5 h along a straight road if her average speed is 18 km/h?

EXAMPLE #3 If a car is traveling at an average speed of 60. meters per second, how long does it take to travel 12 meters?

If a car is traveling at an average speed of 24 m/s for 3 s and 48 m/s for 3 s. What is the average speed for the entire 6 seconds? EXAMPLE #4

A train travels between the 100. meter marker and the 250. meter marker in 10. seconds. What is the train’s average speed? EXAMPLE #5

Average Acceleration Acceleration is the RATE at which VELOCITY changes. A truck accelerates from 10 m/s to 30 m/s in 2.0 seconds. What is the acceleration? Suppose the same truck then slows down to 5 m/s in 4 seconds. What is the acceleration? “m/s/s” or “m/s 2” is the derived unit for acceleration.

Q: You are driving a car. Which of the following will allow you to accelerate the car? A) Gas Pedal B) Brake C) Steering Wheel D) Cruise Control

Scalar vs. Vector Scalar QuantitiesVector Quantities

What do the “signs”( + or -) mean? QuantityPositiveNegative DisplacementYou are traveling north, east, right, up, or in the +x or +y direction. You are traveling south, west, left, down, or in the –x or –y direction. VelocityThe rate you are traveling north, east, right, up, or in the +x or +y direction. The rate you are traveling south, west, left, down, or in the – x or –y direction. AccelerationYour velocity (speed) is increasing in a positive direction or is decreasing in a negative direction. Your velocity (speed) is decreasing in a positive direction or is increasing in a negative direction.

The Acceleration Due to Gravity “a g or g”

Consider an object thrown straight up into the air. (Neglect Air Resistance) 1.As the object is thrown is the velocity positive or negative? 2.As the object rises, what is happening to the speed of the object? Why? 3.At the highest point the object reaches, what is its speed, velocity, and acceleration? 4.What are some things you can say about the object if it is caught at the same height it was thrown?