Kinematics: How things move!Kinematics: How things move!

Velocity and AccelerationVelocity and Acceleration

Motion: KinematicsMotion: Kinematics

The study of motion is known in the The study of motion is known in the physics world as kinematics. Kinematics physics world as kinematics. Kinematics describes motion by using words, describes motion by using words, diagrams, numbers, graphs and equations. diagrams, numbers, graphs and equations. Vectors, scalars, distance, displacement, Vectors, scalars, distance, displacement, speed, velocity and acceleration are all speed, velocity and acceleration are all words often used to describe the motion of words often used to describe the motion of objects. objects.

Kinematics is concerned with the Kinematics is concerned with the motions of objects without being motions of objects without being concerned about what causes the concerned about what causes the motion. We'll only touch motion in motion. We'll only touch motion in one dimension for this unit and leave one dimension for this unit and leave two dimensions for latertwo dimensions for later

Frame of ReferenceFrame of Reference

An important concept we need for talking An important concept we need for talking about the motion of object is the one of about the motion of object is the one of ''frame of referenceframe of reference'. When you are on '. When you are on the school bus, the person sitting in front the school bus, the person sitting in front of you is not moving when compared to of you is not moving when compared to you. When you look out the window at the you. When you look out the window at the road it is obvious that you are moving with road it is obvious that you are moving with respect to it. What is different in each case respect to it. What is different in each case is the is the frame of referenceframe of reference..

Now before we can really talk about moving Now before we can really talk about moving from place to place we need to be able to from place to place we need to be able to describe where exactly we are at any time. describe where exactly we are at any time. This is known as This is known as positionposition. In order to . In order to describe positions we need a reference describe positions we need a reference point point

The reference point can be anywhere you The reference point can be anywhere you wish it to be. We usually place it somewhere wish it to be. We usually place it somewhere to make the math easy. The best spots are to make the math easy. The best spots are usually the starting point of your trip, usually the starting point of your trip, ground level etc. ground level etc.

Here are two examples involving a Here are two examples involving a well. Notice how the values of the well. Notice how the values of the y-positions change as we change y-positions change as we change

the reference point (zero line). the reference point (zero line).

Example 1Example 1

-The reference -The reference point (zero line) is point (zero line) is placed at 'ground' placed at 'ground' level.level.-Positions of the -Positions of the ball below the zero ball below the zero line are negative.line are negative.-Positions of the -Positions of the ball above the zero ball above the zero line are positive.line are positive.

Example 2Example 2

- The reference point The reference point (zero line) is placed (zero line) is placed at the lowest point.at the lowest point.

- All positions of the All positions of the ball are positiveball are positive

Usually when talking about direction, up, Usually when talking about direction, up, north, east and right indicate positive north, east and right indicate positive directions and down, south, west and left directions and down, south, west and left indicate negative directions. indicate negative directions.

Regardless of where we place the Regardless of where we place the reference point, the reference point, the changechange in any two in any two positions in either picture above is always positions in either picture above is always the same. In both cases you should find the same. In both cases you should find that the change is 20 m. This idea is true that the change is 20 m. This idea is true in a any situation.in a any situation.

Vectors and ScalarsVectors and Scalars

A study of motion will involve the A study of motion will involve the introduction of a variety of quantities introduction of a variety of quantities which are used to describe the physical which are used to describe the physical world. Examples of such quantities include world. Examples of such quantities include distance, displacement, speed, velocity, distance, displacement, speed, velocity, acceleration, force, mass, momentum, acceleration, force, mass, momentum, energy, work, power, etc. All these energy, work, power, etc. All these quantities can be divided into two quantities can be divided into two categories - vectors and scalars.categories - vectors and scalars.

SCALARSSCALARS

Scalars can be completely Scalars can be completely described by a magnitude value.described by a magnitude value.

VECTORSVECTORS

A vector quantity is described A vector quantity is described completely only if both its magnitude completely only if both its magnitude and direction are describedand direction are described

Scalar vrs. VectorScalar vrs. Vector

Distance Distance • 15 km15 km

Speed Speed • 30 m/s30 m/s

Time Time • 10s10s

MassMass• 6 kg6 kg

DisplacementDisplacement• 15 km [N 45 E]15 km [N 45 E]

VelocityVelocity• 30 m/s [S]30 m/s [S]

AccelerationAcceleration• 9.81 m/s [down]9.81 m/s [down]

Motion TermsMotion Terms Position Position

• Locates an object within the frame of referenceLocates an object within the frame of reference• symbol: dsymbol: d• Indicates location of object from the reference point. It is Indicates location of object from the reference point. It is

possible to have a negative valuepossible to have a negative value

DisplacementDisplacement• Symbol: Symbol: ΔΔdd• The distance from an initial position to the finishing positionThe distance from an initial position to the finishing position• ΔΔd = dd = dff – d – dii • This change in position is actually given its own name. It is This change in position is actually given its own name. It is

called the called the displacementdisplacement. It is different than what we usually . It is different than what we usually call distance. With distance we don't care where the reference call distance. With distance we don't care where the reference point is but with displacement we do. point is but with displacement we do.

Displacement and VelocityDisplacement and Velocity

Diagrams allow you to describe motion Diagrams allow you to describe motion qualitativelyqualitatively. We describe motion . We describe motion quantitativelyquantitatively by taking measurements by taking measurements

Two fundamental measurements involved in Two fundamental measurements involved in motion are distance and time. Using this you can motion are distance and time. Using this you can calculate an object’s position, speed and rate of calculate an object’s position, speed and rate of change of speed at any particular timechange of speed at any particular time

Displacement ProblemDisplacement Problem

A squirrel starts at the curb and tries A squirrel starts at the curb and tries to scamper straight across a road. It to scamper straight across a road. It runs out 8 m, sees a dog on the runs out 8 m, sees a dog on the other side of the road and runs back other side of the road and runs back 3 m before being flattened by a 3 m before being flattened by a truck. What was the squirrel's truck. What was the squirrel's displacement?displacement?

Displacement SolutionDisplacement Solution

reference point: the starting reference point: the starting point of the trip. This is why I've point of the trip. This is why I've labelled the starting curb as labelled the starting curb as x=0.x=0.

The squirrel starts at the curb The squirrel starts at the curb (x1) and 'finishes' at x2. We (x1) and 'finishes' at x2. We know that x1=0 since that is know that x1=0 since that is our zero line so we just need our zero line so we just need the value of x2. A little the value of x2. A little inspection should reveal that inspection should reveal that x2=5 m. The squirrel's x2=5 m. The squirrel's displacement is then displacement is then

(No squirrels were harmed in (No squirrels were harmed in the construction of this the construction of this example.)example.)

Example 2Example 2

While waiting for someone I pace 5 While waiting for someone I pace 5 m east, 4 m west, another 2 m west, m east, 4 m west, another 2 m west, and 3 m east. What was my and 3 m east. What was my displacement from my starting point?displacement from my starting point?

Time and Time IntervalsTime and Time Intervals• The elapsed time between two instants The elapsed time between two instants

VelocityVelocity• Scalar - SpeedScalar - Speed

Distance travelled divided by the time spent Distance travelled divided by the time spent travellingtravelling

Speed = distance /timeSpeed = distance /time

• Vector – VelocityVector – Velocity How fast the object is moving including the direction How fast the object is moving including the direction Rate of change in positionRate of change in position Average velocity = displacement /timeAverage velocity = displacement /time