Motion in a Straight Motion in a Straight LineLine

PositionVelocity

Acceleration

Name Some Things That Name Some Things That MoveMove

Vehicles – cars, planes, etc. Animals – birds fly…fish swim…

people walk Molecules – vibrational, rotational

and translational motion The Earth, the moon, the sun, the

Galaxy…the universe …everything moves…maybe…

So…then, what is motion?

Motion is common to everything in the universe.

That is why it is the beginning of the study of physics.

Motion is described by three criteria: position, velocity and

acceleration.

POSITIONPOSITION

Must be defined relative to a reference point.

Must be defined using both magnitude and direction.

Displacement and Displacement and DistanceDistance

A objects displacement is defined as the separation between an object and a reference point.

It must be defined by magnitude and direction.

… and Distance?

Distance is simply the separation between any two points.

It is defined simply by magnitude.

Scalars and VectorsScalars and Vectors

What is a Scalar?What is a Scalar?

A scalar is a quantity that is described only by magnitude…such as distance.

The distance from Gainesville to Bronson is 22 miles.

What Is a Vector?What Is a Vector?

A vector is a quantity that must be described by magnitude and direction.

The displacement between Gainesville and Bronson is 22 miles at 32 degrees south of west.

Speed and VelocitySpeed and Velocity

The relationship between motion and

time.

SpeedSpeed

Speed is defined as the distance traveled per unit time.

It is a scalar quantity.

It units are meters per second (m/s).

t

ds

VelocityVelocity

Velocity is displacement per unit time.

It is a vector quantity.

Its units are meters per second (m/s).

t

dv

if

if

tt

dd

t

dv

More VelocityMore Velocity

It is defined relative to a reference point.

Velocity describes both speed and direction.

Depending on your direction, it can be negative or positive.

Now Remember This

Velocity is a vector quantity. Speed is a scalar quantity. Displacement is a vector

quantity. Distance is a scalar quantity.

DefinitionsDefinitions

Average Velocity

Instantaneous Velocity

Relative Velocity

AccelerationAcceleration

Consider an airplane taking off. As it goes down the runway it

increases its speed until it is going fast enough to

“lift off” the ground.

Son of AccelerationSon of Acceleration

The increase of velocity per unit time is called acceleration.

It is the rate of change of velocity.

Its units are meters per second squared (m/s^2).

Average Average AccelerationAcceleration

Average acceleration is the change in velocity divided by

the change in time.

t

vv

t

va if

…and some notes… Acceleration

is a vector. It can be

positive or negative.

At rest means initial time is zero.

When velocity is constant, acceleration is zero.

When velocity increases at a constant rate, acceleration is uniform.

The Motion The Motion EquationsEquations

2if

if

if

vvv

atvvt

vva

tvv

d

tvd

if

2

Displacement & Acceleration

By factoring out final velocity, we can get displacement in terms of initial velocity and uniform acceleration.

22

1 attvd i

……and what if you don’t and what if you don’t have time?have time?

Let’s factor time out of the equation and see what we get…

advv if 222

In SummationIn Summation

Now we have equations that will enable us to

solve for time, velocity, displacement and acceleration for

horizontal straight line motion.

……but wait a but wait a minute…minute…

What if it’s vertical straight line motion…

say, like a rocket going up at Cape Canaveral?!?

It’s really quite It’s really quite simplesimple

When you are traveling in a vertical direction, acceleration is always the same.

It is the acceleration of gravity, g, which always has the same value.

GRAVITYGRAVITY

2/80.9 smg

Vertical Motion

For vertical motion problems, simply substitute g for a in

any of the straight-line motion equations.