Distance

The length an object actually travels.

How far you go.

Scalar

Displacement

The change in position of an object.

Length between start and finish

Vector

Average Velocity

average velocity = change in position

change in time =

displacement

time interval

f iavg

f i

x xxv

t t t

Velocity vs. Speed• Velocity describes motion with both a

direction and a numerical value (i.e. magnitude). (vector)

• Speed has no direction, only magnitude.

• Average speed is equal to the total distance traveled divided by the time interval. (scalar)

distance traveledaverage speed =

time of travel

Sign Conventions for Velocity

Interpreting Velocity Graphically

The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.

The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object’s path.

Acceleration

Units for acceleration are 1 m/s/s or m/s2 This means that every second you increase your velocity by one m/s.

change in velocityaverage acceleration =

time required for change

Changes in Velocity

• Acceleration is the rate at which velocity changes over time.

f iavg

f i

v vva

t t t

• An object accelerates if its speed, direction, or both change.

• Acceleration has direction and magnitude. Thus, acceleration is a vector quantity.

Acceleration

Changes in Velocity• Consider a train moving to the right, so that the

displacement and the velocity are positive.• The slope of the velocity-time graph is the

average acceleration.

– When the velocity in the positive direction is increasing, the acceleration is positive, as at A.

– When the velocity is constant, there is no acceleration, as at B.

– When the velocity in the positive direction is decreasing, the acceleration is negative, as at C.

Graphical Representations of Acceleration

Practice• A car accelerates east from rest to a final

velocity of 20 m/s east in a time interval of 5.0 s. What is the average acceleration of the car?

Practice• A car traveling initially at +3.0 m/s

accelerates to 24 m/s during an interval of 20 s. What is the acceleration during this time?

There Are Other Uses for the Formula

vf = vi + atFinal Velocity = Initial Velocity + Acceleration x Time

Practice• A car traveling initially at +3.0 m/s

accelerates at the rate of +1.20 m/s2 for an interval of 20 s. What is the velocity at the end of the acceleration?

Velocity and Acceleration

Objectives• Relate the motion of a freely falling body to

motion with constant acceleration.

• Calculate displacement, velocity, and time at various points in the motion of a freely falling object.

• Compare the motions of different objects in free fall.

Free Fall

Free Fall• Free fall is the motion of a body when only the

force due to gravity is acting on the body.

• The acceleration on an object in free fall is called the acceleration due to gravity, or free-fall acceleration.

• Free-fall acceleration is denoted with the symbols ag (generally) or g (on Earth’s surface).

Free-Fall Acceleration

Free-Fall Acceleration• Free-fall acceleration is the same for all

objects, regardless of mass.• we use the value g = 9.8 m/s2.• Free-fall acceleration on Earth’s surface is

–9.8 m/s2 at all points in the object’s motion.

Free-Fall Acceleration

• Consider a ball thrown up into the air.– Moving upward: velocity is decreasing,

acceleration is –9.8 m/s2

– Top of path: velocity is zero, acceleration is –9.8 m/s2

– Moving downward: velocity is increasing, acceleration is –9.8 m/s2

Velocity and Acceleration of an Object in Free Fall

Newton’s First Law

• An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a straight line) unless the object experiences a net external force.

• In other words, when the net total external force on an object is zero, the object’s acceleration is zero. (i.e. the change in the object’s velocity is zero)

Newton’s Second Law

The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass.

F = manet force = mass acceleration

F represents the vector sum of all external forces acting on the object, or the net force.

Newton’s Second Law

Newton’s Third Law

• If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction.

• In other words, for every action, there is an equal and opposite reaction.

• Because the forces coexist, either force can be called the action or the reaction.

Action and Reaction Forces• Action-reaction pairs do not imply that the net

force on either object is zero. • The action-reaction forces are equal and opposite,

but either object may still have a net force on it.

Consider driving a nail into wood with a hammer. The force that the nail exerts on the hammer is equal and opposite to the force that the hammer exerts on the nail.

But there is a net force acting on the nail, which drives the nail into the wood.

Newton’s Third Law

Weight• The gravitational force (Fg) exerted on an

object by Earth is a vector quantity, directed toward the center of Earth.

• The magnitude of this force (Fg) is a scalar quantity called weight.

• Weight changes with the location of an object in the universe.

Weight, continued

• Calculating weight at any location:

Fg = mag

ag = free-fall acceleration at that location

• Calculating weight on Earth's surface: ag = g = 9.81 m/s2

Fg = mg = m(9.81 m/s2)

Gravity as a Force

• The gravitational force (Fg) exerted on an object by Earth is a vector quantity, directed toward the center of Earth.

• Force is in Newtons• Masses are in kg• Distance is in meters

Gravity as a Force

• The gravitational force constant is G• G = 6.67 x 10-11 N-m2/kg2

• The masses are simply the mass of the two gravitational bodies (i.e. your mass and the earth’s)

• When using G and ME, then it simplifies to g