Speed & Velocity

Linear Motion Linear motion: motion in a single dimension Moving in a straight line Ex: riding in a car without your hands on the steering wheel Non-ex: making a turn around a corner

Rates Rate: A quantity divided by time A rate tells how quickly something happens miles per hour, words per minute, meters per second Ex: speed (meters per second), acceleration (meters per second per second) Non-ex: distance (meters), time (seconds)

Motion is Relative Frame of Reference: point of view of the observer If something is relative, it depends on the frame of reference. Usually, when we discuss the speeds of things on Earth, we mean the speed with respect to the Earth’s surface.

Speed Speed: the distance covered per unit of time. Speed is a measure of how fast something is moving. the rate at which distance is covered. Speed: the distance covered per unit of time. SI unit: m/s Ex: 100 km/hr, 55 mph, 30 m/s Equation: v = d / t v = speed (m/s) d = distance (m) t = time (s)

Types of Speed Instantaneous speed Average speed the speed at any given instant Ex: speedometer; radar gun Average speed the total distance covered divided by the time Average speed does not indicate changes in the speed that may take place during a trip. BOTH instantaneous and average speeds indicate the rate at which distance is covered.

Physics Problem Solving Strategy List your variables Givens Unknown variable If need be, convert variables to SI units Choose the equation that matches your variables Substitute variables in to the equation Solve

Check Your Understanding If a cheetah can maintain a constant speed of 25 m/s, it covers 25 meters every second. At this rate, how far will it travel in 10 seconds? d = ? v = 25 m/s t = 10 s v = d /t 25 m/s = (d) / (10s) d = (25 m/s)(10s) d = 250m

Check Your Understanding How about in one minute? d = ? v = 25 m/s t = 60s **Convert minutes  seconds** v = d / t 25 m/s = (d) / (60s) d = (25 m/s)(60s) d = 1500m

Velocity Velocity: the speed in a given direction SI unit: m/s Ex: 100 km/hr East, 55 mph North, 30 m/s Southwest Equation: v = d / t v = velocity (m/s) d = distance (m) t = time (s)

Speed vs Velocity When we say that a car travels 60km/hr, we are indicating its speed. When we say that a car is traveling 60km/hr to the north, we are indicating its velocity. Speed is a description of how fast an object moves; velocity is how fast it moves AND in what direction .

Check Your Understanding The speedometer of a car moving northward reads 100 km/h. It passes another car that travels southward at 100 km/h. Do both have the same speed? Do they have the same velocity? Both cars have the same speed, but they have opposite velocities because they are moving in opposite directions.

Types of Velocity Constant Velocity requires both constant speed and constant direction (moving in a straight line)

Types of Velocity Changing Velocity 3 ways to change velocity Increase speed Decrease speed Change direction Constant speed and constant velocity are NOT the same thing. Ex: A body may move with constant speed around a curved path, but it does not move with constant velocity b/c the direction changes at every instant.

Scalar Quantities Scalar: a quantity that requires magnitude only Number and units ONLY; no direction Ex: Speed, mass, time Non-ex: Velocity

Vector Quantities Vector: a quantity that requires both magnitude AND direction Number, units, AND direction Ex: Velocity, acceleration, force Non-ex: Speed, temperature

Check Your Understanding Is height a vector or a scalar quantity? Scalar. Height only includes magnitude (how big the number is) only and NOT direction. You are 5’8” tall, not 5’8” to the east.

Vector Quantities An arrow is used to represent the magnitude & direction of a vector quantity. The length of the arrow indicates the magnitude (size) of the vector quantity. The direction of the arrow represents the direction of the vector quantity. 10 m to the right 50 m to the left

Adding Vectors When more than one vector combines together, both the magnitude AND the direction matter. The sum of 2 or more vectors is called the resultant. Draw the arrows tip to tail The tail of the first arrow should be at the origin (at the beginning) Place the tail of the next arrow at the tip of the first The straight line from the tail of the first arrow to the tip of the last arrow is the resultant vector

+ = Adding Vectors Arrows both point in the same direction Draw the arrows tip to tail The tail of the first arrow should be at the origin (at the beginning) Place the tail of the next arrow at the tip of the first Add together to find the resultant Ex: 4 m/s E + 3 m/s E = 7 m/s E + =

+ = Adding Vectors Arrows point in opposite directions Draw the arrows tip to tail The tail of the first arrow should be at the origin (at the beginning) Place the tail of the next arrow at the tip of the first Subtract to find the resultant Ex: 4 m/s E - 3 m/s W = 1 m/s E + =

+ = Adding Vectors When arrows are not in one dimension Draw the arrows tip to tail The tail of the first arrow should be at the origin (at the beginning) Place the tail of the next arrow at the tip of the first The straight line from the tail of the first arrow to the tip of the last arrow is the resultant + =

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Check Your Understanding A boy is riding his bike down the street at a speed of 10 m/s. A gust of wind came out of nowhere headed towards the boy. If the wind is traveling 3 m/s, what will the boy’s new speed be? Since the boy and the wind are moving in opposite directions, we need to subtract their speeds to find the resultant. 10 m/s – 3 m/s = 7 m/s

Position Time Graphs Position Time graphs show the distance covered over an elapsed time Aka Distance Time graphs and Displacement Time graphs Time is always the independent variable Position (distance) is always the dependent variable

Position Time Graphs The slope of a Position-Time graph is equal to velocity Slope = rise / run Slope = position / time Velocity = position / time

Position Time Graphs Slope of a position-time graph The steeper the slope, the faster the velocity A positive slope is forward motion A negative slope is moving backwards A zero slope is NOT moving at all

Check Your Understanding Which person is moving faster, the red or blue jogger? The red jogger. The red jogger’s line has a steeper slope and therefore a faster speed.

Check Your Understanding Are both joggers moving forwards or backwards? Forwards. The slope is positive, so the distance increases as the time increases.

Check Your Understanding At what time does Person B pass Person A? At 45 seconds. The lines intersect at this time and both runners are at the same position at the same time.