Chapter 11 Motion

11.1 Distance and Displacement

Choosing a Frame of Reference To describe motion, one must state 1. the direction the object is moving 2. how fast the object is moving 3. the location of the object at a certain time

A FRAME OF REFERENCE is a system of objects that are not moving with respect to one another Ex. fly in moving car How fast an object is moving depends on the frame of reference one chooses  

RELATIVE MOTION is movement in relation to a frame of reference   Typically, the frame of reference for objects on Earth is Earth itself (the ground); usually the Earth is assumed to be still. Is it?

DISTANCE is the length of a path between two points   SI unit- meter (cm or km)

DISPLACEMENT is the direction from the starting point and the length of a straight line from the starting point to the ending point Displacement is a vector quantity

A VECTOR is a quantity that has both magnitude (size, length, amount-a number) and direction (up, down, left, right, N, S, E, W, etc.) Arrows can be used to represent vectors; the direction of the arrow represents the direction of the vector, while the size of the arrow represents the magnitude of the vector Ex. 2 km E, 4 km W; SEE FIG. 3, P. 330

The direction of a vector can be represented by the sign (+ or -); assigned arbitrarily (at random, must be consistent) Ex. 2 km E, 4 km W

The RESULTANT VECTOR is the vector sum of two or more vectors SEE FIG. 3, 4, PP. 330, 331 Vectors can be added 1. ALGEBRAICALLY-add vectors, assigning signs to directions 2. GRAPHICALLY-draw first vector (with direction), draw second vector with tail starting at head of first vector; resultant is a vector drawn from tail of first vector to head of last vector

What is the resultant of the following vectors: a. 5 km E, 8 km E   b. 10 km N, 30 km S c. 5 m left, 6 m right d. 2 m N, 5 m W

11.2 Speed and Velocity

Examples How far will a car traveling at 100 km/h travel in 2.8 h?   How long will it take the car in the example above to travel 350 km (moving at 100 km/h)? If the car takes 3 hours to travel to the next city, which is 350 km away, how fast is the car moving?

SPEED is the ratio of the distance an object moves to the amount of time the object moves; in SI base units, measured in m/s  There are two ways two ways to express speed 1. AVERAGE SPEED-computed for entire duration of trip v = d/t where v is average speed (usually in m/s), d is total distance traveled (in m), and t is total time (in s) SEE “Math Skills-Calculating Average Speed” p. 333

Ways to express speed 2. INSTANTANEOUS SPEED-rate at which an object is moving at a given moment in time Ex. speedometer SEE FIG. 6, P. 334

 VELOCITY is the speed and direction in which an object is moving; VELOCITY IS A VECTOR (magnitude and direction)   A change in velocity can be the result of a change in speed, change in direction, or both

An object moves with CONSTANT VELOCITY if it moves in a straight line at a constant speed   Since velocity is a vector, two or more velocities can be added by vector addition

A boat moves with the current of a river at a speed of 12 km/h A boat moves with the current of a river at a speed of 12 km/h. The speed of the current is 5 km/h. What is the resultant velocity of the boat relative to the riverbank? SEE FIG. 10, P. 337 The boat in the example above turns around and moves upstream at 12 km/h. What is the resultant velocity of the boat relative to the riverbank? SEE FIG. 10, P. 337 The boat in the examples above turns and moves toward the riverbank at 12 km/h. What is the resultant velocity of the boat relative to the riverbank?

11.3 Acceleration

ACCELERATION (a) is any change in velocity; includes changes in speed and/or direction. NOTE-acceleration is a vector, measured in (m/s)/s or m/s2 If an object is SLOWING DOWN called DECELERATION

An object is in FREE FALL when the movement of the object toward Earth is solely because of gravity Objects near Earth’s surface accelerate downward at the ACCELERATION DUE TO GRAVITY, g g = 9.8 m/s2

SEE FIG. 12, P. 343 If an object is dropped, after 1 s it will be traveling at 9.8 m/s downward; after 2 s it will be traveling 19.6 m/s; after 3 s it will be traveling 29.4 m/s Recall units for velocity: m/s acceleration: m/s/s or m/s2

Objects are accelerating 1. because of a change in direction Ex. carousel 2. because of a change in speed and direction Ex. roller coaster

CONSTANT ACCELERATION is a constant change in velocity; how much the velocity changes per second stays the same Does a car going from 0 to 60 mph undergo constant acceleration?

For an object with constant acceleration in a straight line a = (vf – vi)/t where a is acceleration (in m/s2), vf is final velocity (in m/s), vi is initial velocity (in m/s), and t is time (in s) Ex. SEE “MATH SKILLS-CALCULATING ACCELERATION” P. 346

Examples What is the acceleration of a car that reaches a velocity of 20 m/s in 7 s, if it starts from rest? What is the velocity of a rock dropped from a height of 50 m after 2 s?  

INSTANTANEOUS ACCELERATION is acceleration at a given instant; how fast a velocity is changing at a specific instant   SECTION 11.3 ASSESSMENT