Objectives 2-1 to Describe the motion of an object relative to a particular frame of reference. 2.Define and calculate displacement (Δx) as the change in position of an object. 3.Differentiate between a vector quantity and a scalar quantity and state which quantities used in kinematics are vector quantities and which are scalar quantities. 4.Define and calculate speed and velocity. 5.Distinguish between speed and velocity. 6.Describe cases where average speed does not equal average velocity. 7.Describe a situation when the velocity is negative. 8.Interpret and analyze a position vs. time graphs for motion. 9.Solve problems involving speed and velocity.

Warm Up What do you think of when you hear the terms frame of reference and speed?

Activity View the car at the demo table. How could you determine the car’s position? How could you determine the car’s speed? How could you determine the car’s velocity?

Kinematics Describes motion while ignoring the agents that caused the motion

2-1 Reference Frames and Displacement Any measurement of position, distance, or speed must be made with respect to a reference frame. For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher.

Kinematics Problem Solving Always choose a reference point. The object’s position is its location with respect to a chosen reference point

2-1 Reference Frames and Displacement We make a distinction between distance and displacement. Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Distance traveled (dashed line) is measured along the actual path.

Where? Position—reference point needed Distance versus Displacement Period 1 start here.

Position, Distance, Displacement Position—reference point needed Distance—no reference point needed Displacement—change in position

Position/distance/displacement Uses many variables depending on the situation. d = “distance” = generic, any direction x = in the “x-axis”; sometimes considered the “ground”/”floor” or horizontal motion y = in the “y-axis”; sometimes considered the “air/sky” or vertical motion s = around the perimeter of a circle

2-1 Reference Frames and Displacement The displacement is written: Left: Displacement is positive. Right: Displacement is negative.

Scalar and Vector Period 5 Starts here Scalar—quantity that only has a magnitude (distance is an example) Vector—quantity that has a magnitude and a direction (displacement is an example)

What is “moving”? An object is moving if its position relative to a fixed point is changing. Ex. Space shuttle is moving at 30 kilometers per second relative to the sun or 8 km/s relative to the earth.

2-2 Average Velocity Speed: how far an object travels in a given time interval Velocity includes directional information: (2-1)

Speed and Velocity Speed—scalar value (has size only); describes distance traveled per unit of time. Velocity—vector value (has size and direction); describes displacement per unit of time.

In racing, is it possible for the car with the greatest speed crossing the finish line to lose the race? Explain. For both cars, the time elapsed is the distance traveled divided by the average velocity. Since both cars travel the same distance, the car with the larger average velocity will have the smaller elapsed time.

Constant velocity Constant speed and constant direction. Does this motion show constant speed or constant velocity?

Position – Time Graph

Independent variable “x” Dependent variable (“y”) v d t

Formula to find the slope of a line

What would the drop of the slope indicate about the motion?

What is the velocity of this object? The slope of a position versus time graph is its velocity!

Slope = -3.0 m/s Using the two given data points, the rise can be calculated as m (the - sign indicates a drop). The run can be calculated as 8.0 seconds. Thus, the slope is -3.0 m/s. The drop indicates the opposite direction which would be backwards or left.

What does this imply about the person’s motion? distance time

#6 page 39 A particle at t 1 = -2.0 s is at x 1 = 3.4 cm and at t 2 = 4.5 s is at x 2 = 8.5 cm. What is its average velocity? Can you calculate its average speed from these data?

#9 page 39 A person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min? Calculate (a) the average speed and (b) the average velocity, in m/s.

2-3 Instantaneous Velocity The instantaneous velocity is the average velocity, in the limit as the time interval becomes infinitesimally short. These graphs show (a) constant velocity and (b) varying velocity. (2-3)

Given the curve: x f(x) x+h f(x+h)

NUMERICALLY A. Find the average velocity over the interval 1 < t < 3. B. Using appropriate units, explain the meaning of your answer. 0.9 represents the average meters per hour of a particle from t = 1 hour to t = 3 hours

NUMERICALLY A. Find the average velocity over the interval 0 < t < 4 B. Using appropriate units, explain the meaning of your answer represents the average meters per hour of a particle from t = 0 to t = 4 hours

NUMERICALLY A. Estimate the velocity at t = 5. Note: velocity implies INSTANTANEOUS velocity B. Using appropriate units, explain the meaning of your answer. The velocity is approximately meters per hour at t = 5 hours.

GRAPHICALLY Find the average rate of change of f(x) on [-2, 2] Estimate the instantaneous rate of change of f(x) at x = 0

Find the average velocity of the ship in the first two hours Estimate the velocity of the ship after 75 minutes

Closure 1.When did the person stop moving? 2.What happened at 9 minutes? 3.When did he have the greatest speed?

Homework Chapter 2 Problems: 7, 11, 14