Electric Current Notes Motion

Electric Current Notes Motion of What? To simplify things as much as possible, we will first consider one-dimensional motion (motion along a straight line) of particles (points that can’t spin, rotate, flip, flop, or wiggle around).

Describing Motions We will concern ourselves (for now) with describing motion - kinematics. We will worry about explaining motion (dynamics) later.

Two Simple Motions In our course, we will be primarily concerned describing with 2 simple motions: Motion with constant velocity Motion with constant acceleration

Electric Current Notes Position Mark a zero point on the line, pick a direction to be positive, and measure from there. Positions can be positive or negative. Units of position: centimeters, meters, kilometers, inches, feet, miles, etc. Common symbol: x

Operational Definition Position, like other physical quantities, is defined by telling how you go about measuring it - not by giving synonyms or descriptive phrases. This is called an operational definition.

Positions are Relative Electric Current Notes Positions are Relative Different people can mark the line differently, so they can get different numbers for position. The position number (and unit) really don’t mean anything until you specify where you marked “0”, and which way you made positive - your frame of reference.

Electric Current Notes Displacement Displacement = net distance moved or net change in position Common symbol, d or ∆x If you move from xo to x, displacement, d = ∆x = x - xo

Electric Current Notes Rates A rate measures how fast something changes. In physics, a rate is almost always calculated as a quantity divided by time. Rate Q changes = change in Q time for Q to change

Electric Current Notes Speed Speed is the rate position changes, or the rate distance is covered. There are two kinds of speed: Average speed Instantaneous speed

Electric Current Notes Average Speed Average speed = distance traveled Or, average speed = displacement In symbols, v = d or ∆x Units of speed: m/s, km/h, mi/h, etc. time it takes time t t

Electric Current Notes Instantaneous Speed Instantaneous speed is what the speedometer says. It is not measured over a time interval, like average speed.

Constant Speed If an object’s instantaneous speed is always the same value, the object has a constant speed. In this case, average speed = instantaneous speed

Electric Current Notes Velocity Velocity = speed + direction 2 kinds of velocity Average velocity = average speed + direction Instantaneous velocity = instantaneous speed + direction

How Velocity Changes The velocity of an object changes if: It speeds up, or It slows down, or It changes direction.

What Velocity Means An object’s velocity tells you how fast its position is changing. 5 m/s means the object’s position changes by 5 meters each second. 60 mi/hr means that the object’s position changes by 60 mi each hour.

Velocities are Relative Speed and velocity are relative quantities. Different observers, in different frames of reference, can measure different velocities. You measure speed and velocity by comparing two motions.

Electric Current Notes Acceleration Acceleration is the rate velocity (not speed) changes. 2 kinds: Average acceleration Instantaneous acceleration

Electric Current Notes Average Acceleration Ave. Accel. = change in velocity in symbols, a = ∆v Accelerations are not relative quantities. time it takes t

Units of Acceleration Since acceleration is a velocity divided by a time, its units are a distance unit divided by 2 time units. This is commonly written 2 ways: m/s/s = m/s2 km/hr/s = km/hr.s

Constant Acceleration Electric Current Notes Constant Acceleration In many common situations, an object’s acceleration is constant, or at least approximately constant. In this case: Average accel. = instantaneous accel.

Electric Current Notes Free Fall Free fall is motion under the influence of gravity only - no friction or air resistance.

Acceleration in Free Fall Electric Current Notes Acceleration in Free Fall The acceleration of an object in free fall is constant. At the surface of Earth, the free-fall acceleration is about 10 m/s2, or 9.8 m/s2 if you have a calculator (or 32 ft/s2 or 22 mi/hr/s in “English” units).

Electric Current Notes Air Resistance The effect of air resistance is to slow an object down and/or decrease its acceleration.

Electric Current Notes The End

Hooray for graphing and Mr. King too!!!!

d t A B C Graphing ! 1 – D Motion A … Starts at home (origin) and goes forward slowly B … Not moving (position remains constant as time progresses) C … Turns around and goes in the other direction quickly, passing up home

Graphing w/ Acceleration d Graphing w/ Acceleration C B t A D A … Start from rest south of home; increase speed gradually B … Pass home; gradually slow to a stop (still moving north) C … Turn around; gradually speed back up again heading south D … Continue heading south; gradually slow to a stop near the starting point

Tangent Lines t On a position vs. time graph: SLOPE VELOCITY Positive d Tangent Lines t On a position vs. time graph: SLOPE VELOCITY Positive Negative Zero SLOPE SPEED Steep Fast Gentle Slow Flat Zero

Increasing & Decreasing t d Increasing Decreasing On a position vs. time graph: Increasing means moving forward (positive direction). Decreasing means moving backwards (negative direction).

Concavity On a position vs. time graph: d Concavity On a position vs. time graph: Concave up means positive acceleration. Concave down means negative acceleration.

Times when you are at “home” Special Points t d Q R P S Inflection Pt. P, R Change of concavity Peak or Valley Q Turning point Time Axis Intercept P, S Times when you are at “home”

Curve Summary t d B C A D

All 3 Graphs t d v t a t

Graphing Tips t v t d Line up the graphs vertically. Draw vertical dashed lines at special points except intercepts. Map the slopes of the position graph onto the velocity graph. A red peak or valley means a blue time intercept.

Graphing Tips The same rules apply in making an acceleration graph from a velocity graph. Just graph the slopes! Note: a positive constant slope in blue means a positive constant green segment. The steeper the blue slope, the farther the green segment is from the time axis. v t a t

Real life Note how the v graph is pointy and the a graph skips. In real life, the blue points would be smooth curves and the green segments would be connected. In our class, however, we’ll mainly deal with constant acceleration. v t a t

Area under a velocity graph “forward area” “backward area” Area above the time axis = forward (positive) displacement. Area below the time axis = backward (negative) displacement. Net area (above - below) = net displacement. Total area (above + below) = total distance traveled.

Area “forward area” “backward area” t v t The areas above and below are about equal, so even though a significant distance may have been covered, the displacement is about zero, meaning the stopping point was near the starting point. The position graph shows this too. t d

v (m/s) Area units 12 t (s) Imagine approximating the area under the curve with very thin rectangles. Each has area of height  width. The height is in m/s; width is in seconds. Therefore, area is in meters! 12 m/s 0.5 s The rectangles under the time axis have negative heights, corresponding to negative displacement.

Graphs of a ball thrown straight up d The ball is thrown from the ground, and it lands on a ledge. The position graph is parabolic. The ball peaks at the parabola’s vertex. The v graph has a slope of -9.8 m/s2. Map out the slopes! There is more “positive area” than negative on the v graph. t v t a t

Graph Practice Try making all three graphs for the following scenario: 1. Schmedrick starts out north of home. At time zero he’s driving a cement mixer south very fast at a constant speed. 2. He accidentally runs over an innocent moose crossing the road, so he slows to a stop to check on the poor moose. 3. He pauses for a while until he determines the moose is squashed flat and deader than a doornail. 4. Fleeing the scene of the crime, Schmedrick takes off again in the same direction, speeding up quickly.