Describing Motion: Velocity & Acceleration

Some words to know… Position – the separation between an object and a reference point Displacement – change in position A change in distance and direction between 2 positions Motion – relative displacement

Some words to know… Scalar Quantity – quantity represented by only magnitude (a number and unit) Vector Quantity – quantity represented by both magnitude & direction (a number and unit with direction)

Positive & Negative in Physics Positive – when motion is away from the start point, up, right, east or north Negative – when motion is toward the starting point, down, left, west or south

Speed vs. Velocity Average Speed (s): total distance traveled divided by total time interval Scalar quantity Average velocity (v): change in position divided by the total time interval Vector quantity Motion Basics - PHYS

Formula for Velocity v = Δd / Δt Where… v = velocity Δd = displacement (change in position) Δt = change in time UNIT: m/s (meters per second)

What’s the Δ about? v = Δd / Δt Is called, “delta” and means change Δd = df – di (change in position) Δt = tf – ti (change in time) Remember that f = final and i = initial

Instantaneous Velocity The speed and direction at a particular instant in time, like a speedometer in a car

Practice 1. A helicopter ascends at a constant speed of 5 m/s. How far does it rise in 5 seconds?

Acceleration = change in velocity over time Remember – velocity changes when either magnitude OR direction changes!

Formula for Acceleration Where, a = acceleration Δv = change in velocity Δt = change in time UNIT: m/s2 Remember, Δ means “change”

Practice 2) An empty toy wagon reaches the bottom of a hill & rolls onto the level ground with a speed of 1.5 m/s. How long will it take the wagon to come to a stop if its acceleration is -0.6 m/s2?

Practice on your own… Ernie went to see some friends in San Antonio, 240 miles west. It took him 3 hours to get there from Houston. What was his average speed (in mi/h)? What was his velocity (in mi/h)? In training for the Marathon, Rhonda would run 13 miles due north to the Community Center, where she would meet her friend and swim after her run. If Rhonda ran this in 2 hours, what was her velocity? What was her displacement from home? What is the acceleration of a race car if its speed changes from 44 m/s to 66 m/s in 11 seconds? A train moving at a speed of 45 m/s slows to 15 m/s in 12 seconds. What is its acceleration? A plane starting from rest accelerates to 72 m/s during a 5-second period. What is its acceleration?

Ernie went to see some friends in San Antonio, 240 miles west Ernie went to see some friends in San Antonio, 240 miles west. It took him 3 hours to get there from Houston. What was his average speed (in mi/h)? 80 mi/h What was his velocity (in mi/h)? 80 mi/h W In training for the Marathon, Rhonda would run 13 miles due north to the Community Center, where she would meet her friend and swim after her run. If Rhonda ran this in 2 hours, what was her velocity? 6.5 km/h N What was her displacement from home? 13 km N What is the acceleration of a race car if its speed changes from 44 m/s to 66 m/s in 11 seconds? 2 m/s2 A train moving at a speed of 45 m/s slows to 15 m/s in 12 seconds. What is its acceleration? -2.5 m/s2 A plane starting from rest accelerates to 72 m/s during a 5-second period. What is its acceleration? 14.4 m/s2

Motion Graphs – position-time (d/t) Position-time graphs show how the position of an object changes over time. So, the slope of a d/t graph tells us the VELOCITY of the object.

Motion Graphs – velocity-time (v/t) Velocity-time graphs show how the velocity of an object changes over time. So, the slope of a d/t graph tells us the ACCELERATION of the object.

What if the line is curved? The slope is constantly changing, so that means the velocity is changing. Changing velocity is called ACCELERRATION.

Finding displacement on a v/t graph The area under the graph represents displacement (Δd).

Kinematic Equations Mathematical Equations used in motion They are formed from our motion graphs

Another way to calculate acceleration Where… vf= final velocity vi= initial velocity Δd= position a= acceleration

How to calculate displacement Where… Δd= position vi= initial velocity Δt = time a= acceleration

Practice #1 An airplane starts from rest and accelerates at a constant 3 m/s2 for 30 s before leaving the ground. A) How far did it move? B) How fast was it going when it took off?

Practice #2 A race car slows with a constant acceleration of -11 m/s2. If the car is going 55 m/s. A) How long will it take to stop? B) How far did it move?

Practice #3 An object with an initial velocity of 10 m/s is accelerated for 10 seconds at 5 m/s2 A) What is the final velocity? B) How far does the object travel?

Free Fall The “influence” of gravity… An object is in free fall when it is only under the influence of gravity We ignore air resistance The object can be moving upward OR downward For a dropped object, vi = o For a thrown object, velocity at the top of the path = 0 The “influence” of gravity… An acceleration, caused by the attractive force between two objects On Earth, the magnitude of g is 9.8 m/s2 and the acceleration due to gravity (ag) is negative.

How can ag always be negative? In free fall, an object changes its speed by 9.8 m/s every second (9.8 m/s/s). If moving up, it is decreasing its speed 9.8 m/s every second (so, a = -9.8 m/s2) If moving down it is increasing its speed back toward Earth by 9.8 m/s every second (so, a = -9.8 m/s2 ) Motion Basics - PHYS

On motion graphs… Motion Basics - PHYS

Practice A baseball is thrown vertically with a velocity of 12 m/s. What is the maximum height the baseball reaches? How long does it take to reach max height? What is the velocity when it hits the ground?