Chapter 2-Section 11-Dimensional Kinematics

The motion of automobiles, Hot Wheel cars, and rockets are used to illustrate the physics of position, velocity, acceleration, and kinematic graphing.

KinematicsKinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations.

Motion Motion happens all around us. One – dimensional motion is the

simplest form of motion. The object can only move in one

dimension forward and backward left and right up and down

Motion Motion takes place over time and

depends on a frame of reference. Frame of Reference – a coordinate

system for specifying the precise location of objects in space

The choice of a reference point is arbitrary, but once chosen, the same point must be used throughout the problem.

Distance and Displacement Distance and displacement are two

quantities which may seem to mean the same thing, yet they have distinctly different meanings and definitions.

Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.

Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

Distance and Displacement

To test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

Distance traveled = Displacement =12 m 0 m

Distance and Displacement

The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D. Use the diagram to determine the distance traveled by the skier and the resulting displacement during these three minutes.

Distance traveled = Displacement =420 m 140 m

Seymour Butz views football games from under the bleachers. He frequently paces back and forth to get the best view. The diagram below shows several of Seymour's positions at various times. At each marked position, Seymour makes a "U-turn" and moves in the opposite direction. In other words, Seymour moves from position A to B to C to D. What is Seymour's resulting displacement and distance of travel?

Distance = 95 yards Displacement = 55yards

Displacement

Δx = xf – xi

Displacement = change in position

Displacement = final position – initial position

Speed and Velocity

Speed is a scalar quantity which refers to "how fast an object is moving.“

Velocity is a vector quantity which refers to "the rate at which an object changes its position."

Sorry, Ma’am, but you

were doing 45 mph in a

30 mph zone.But I haven’t

driven 45

miles yet.

Okay, okay, would you believe that I haven’t been driving for an hour yet?

Speeding Little Old Lady

Average Speed and Velocity

Average speed is the total distance traveled divided by the time interval

Average velocity is the total displacement traveled divided by the time interval during which the displacement occurred

While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?

Ave speed = 55 mi / h

Ave speed = distance traveled time of travel

Ave speed = 440 mi 8 h

Problem

A car travels from city A to city B (100km). If the first half of the distance is driven at 50 km/h and the second half is driven at 100 km/h , what is the average velocity for the trip?

A B100 km

V = 50 km/h V = 100 km/h

t = d/st = 50 km 50 km/ht = 1 h

t = d/st = 50 km 100 km/ht = 0.5 h

Ave. velocity = displacement time

Ave velocity = 100 km 1.5 h

67 km/h

Velocity Constant Velocity – velocity is unchanging

Instantaneous Velocity – the velocity of an object at some instant (or specific point in its path) (slope)

HomeworkDescribing Motion with Position vs. Time Graphs

The Meaning of Shape for a position-time Graph

The specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a position vs. time graph.If the position-

time data for such a car were graphed, the resulting graph would look like the graph at the right.

If the position-time data for such a car were graphed, the resulting graph would look like the graph at the right.

Positive constant velocity Positive changing velocity

The position vs. time graphs for the two types of motion – constant velocity and changing velocity

The Principle of Slope for a p–t Graph

The slope of the line on a position-time graph reveals useful information about the velocity of the object. It's often said, "As the slope goes, so goes the velocity."

Positive velocity

Positive slope

Constant velocity

Constant slope

Small velocity

Small slope

Let me test your understanding

Match the slope with the velocity

Positive velocity Positive slope

Constant velocityConstant slope

Small velocitySmall slope

Answers :

Slow rightward,Constant velocity

Fast, rightward,Constant velocity

Fast, leftward Constant velocity

Slow , leftward Constant velocity

Leftward velocity,Slow to fast

Leftward velocity,Fast to slow

The Passing Lane

Constant Positive Velocity

Constant Negative Velocity