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

Motion Basics - PHYS

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

Formula for Velocity

Where… v = velocityΔd = displacement (change in

position)Δt = change in time UNIT: m/s (meters per second)

v = Δd / Δt

What’s the Δ

about?

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

v = Δd / Δt

Instantaneous VelocityThe speed and direction at a

particular instant in time, like a speedometer in a car

Practice1. 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 = accelerationΔv = change in velocityΔt = change in time UNIT: m/s2

Remember,

Δ means “change”

t

v

t

vva if

Practice2) 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?

1) Ernie went to see some friends in San Antonio, 240 miles west. It took him 3 hours to get there from Houston.

a) What was his average speed (in mi/h)? 80 mi/hb) What was his velocity (in mi/h)? 80 mi/h W

2) 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.

a) If Rhonda ran this in 2 hours, what was her velocity? 6.5 km/h N

b) What was her displacement from home? 13 km N

3) 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

4) 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

5) A plane starting from rest accelerates to 72 m/s during a 5-second period. What is its acceleration? 14.4 m/s2

Practice on your own…

Motion Graphs – position-time (d/t)

Position-time graphs show how the position of an object changes over time.

t

d

x

y line of slope

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.

t

v

x

y line of slope

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= positiona= acceleration

d

vva if

2

22

How to calculate displacement

Where…Δd= positionvi= initial velocity

Δt = timea= acceleration

2

2

1tatvd i

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 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.

Motion Basics - PHYS

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…

PracticeA 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?