Kinematics

• Kinematics is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion.

• We will learn to describe motion in three ways.– Using words– Using graphs– Using equations

Particle

• A particle is an object that has mass but no volume and occupies a position described by one point in space.

• Physicists love to turn all objects into particles, because it makes the math a lot easier.

Position

• How do we represent a point in space?a) One dimension

b) Two dimensions

c) Three dimensions

As an object moves, its position undergoes change

Two quantities describe changing position

Distance DisplacementVS

The length of the path traveled

The length and direction of a straight line path from the beginning to the end positiondistance

displacement

Sometimes the path traveled is a straight line

distance = displacement

Displacement will never be greater than distance

Distance (d)

• The total length of the path traveled by a particle is called distance.

• “How far have you walked?” is a typical distance question.

• The SI unit of distance is the meter.

Displacement• The change in the position of a particle in a certain

direction• Δ is a Greek letter used to represent “change in “. Δx

therefore means “change in x”. It is always calculated by the final value minus the initial value

• “How far are you from home” is a typical displacement question

• The SI unit for displacement is the meter• Calculation of displacement

f ix x x

A

B

50 mdisplacement

100 m

distance

Distance vs Displacement

• A picture can help you distinguish between distance and displacement.

STOP

Vectors and scalars Quantities that have both size, also called magnitude, and direction, are called vectors. Displacement is a change in position in a certain direction. It is a vector quantity. Quantities that are just magnitude, numbers without any direction, such as distance, time, or temperature, are called scalars.

In one dimensional motion, the displacement direction is often given

as positive(+) or negative( -)

A displacement of +3.5 m implies movement of3.5 m in the positive direction.

A displacement of -3.5 m implies movement of3.5 m in the negative direction.

Positive and negative directions are chosen arbitrarily, but usually agree with

standard mathematical conventions.

Question

True or False: An object can be moving for 10 seconds and still have zero displacement.

a. True b. false

If the above statement is true, then describe an example of such a motion. If the above statement is false, then explain why it is false.

QuestionA cross-country skier moves from location A to location B to location C to location D. Each leg of the back-and-forth motion takes 1 minute to complete; the total time is 3 minutes.

a. What is the distance traveled by the skier during the three minutes of recreation?

b. What is the net displacement of the skier during the three minutes of recreation?

Example You are driving a car on a circular track of diameter 40 meters. After you have driven around 2 ½ times, how far have you driven, and what is your displacement?

The average velocity of an object is defined asthe ratio of its change in position to thetime taken to change the position.

vv = average velocity; in units of m/s

=x

x = change in position, or displacement; in units of m

t

t = change in time; in units of s

It is the rate at which

displacement occurs

Velocity is a vector quantity

A positive sign indicates movementin the positive direction.

A negative sign indicates movement in the negative direction.

The “sign” of the velocity indicatesthe direction of movement.

Speed is the magnitude of velocity.

It is a scalar and has no direction given with it.Average speed is the total distance traveled

divided by the total time taken.

Average velocity is the total displacement divided by the total time taken.

Average speed and average velocity are not always equivalent because total distance and total displacement are not always

the same.

Speed is the absolute value of velocity.It is always a positive value.

Example How long will it take the sound of the starting gun to reach the ears of the sprinters if the starter is stationed at the finish line for a 100 m race? Assume that sound has a speed of about 340 m/s.

ExampleYou drive in a straight line at 10 m/s for 1.0 km, and then you drive in a straight line at 20 m/s for another 1.0 km. What is your average velocity?

Acceleration (a)

• Any change in velocity over a period of time is called acceleration.

• The sign (+ or -) of acceleration indicates its direction.

• Acceleration is occurring when an object…– speeds up– slows down– Turns (changes direction)

Questions

• If acceleration is zero, what does this mean about the motion of an object?

• Is it possible for a racecar circling a track to have zero acceleration?

Average Acceleration.In AP Physics B we only consider situations

where acceleration is constant. This allows us to use the following formula

aa = average acceleration; in units of m/s2

= vf

vf = final velocity; in units of m/svi = initial velocity; in units of m/s

t

t = time for the change to occur; in units of s

- vi

vf – vi = change in velocity

Acceleration in 1-D Motionhas a sign!

• If the sign of the velocity and the sign of the acceleration is the same, the object speeds up.

• If the sign of the velocity and the sign of the acceleration are different, the object slows down.

Kinetics Equations

v= useful but not on the AP formula sheet

v =

a= vf

2 = vi2 + 2ax

x = vit +at2

ExampleYou are designing an airport for small planes. One kind of airplane that might use this airfield must reach a speed before takeoff of at least 28 m/s, and can accelerate at 2.00 m/s2. What must the minimum length of the runway be?

ExampleA car traveling at 90 km/h strikes a tree. The front end of the car compresses and the driver comes to a rest after traveling 0.80 m. How long did it take the car to come to a stop?