Kinematics: How things move! Velocity and Acceleration

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

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

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

Now before we can really talk about moving from place to place we need to be able to describe where exactly we are at any time. This is known as position. In order to describe positions we need a reference point Now before we can really talk about moving from place to place we need to be able to describe where exactly we are at any time. This is known as position. In order to describe positions we need a reference point The reference point can be anywhere you wish it to be. We usually place it somewhere to make the math easy. The best spots are usually the starting point of your trip, ground level etc. The reference point can be anywhere you wish it to be. We usually place it somewhere to make the math easy. The best spots are usually the starting point of your trip, ground level etc.

Here are two examples involving a well. Notice how the values of the y-positions change as we change the reference point (zero line).

Example 1 -The reference point (zero line) is placed at 'ground' level. -Positions of the ball below the zero line are negative. -Positions of the ball above the zero line are positive.

Example 2 - The reference point (zero line) is placed at the lowest point. - All positions of the ball are positive

Usually when talking about direction, up, north, east and right indicate positive directions and down, south, west and left indicate negative directions. Usually when talking about direction, up, north, east and right indicate positive directions and down, south, west and left indicate negative directions. Regardless of where we place the reference point, the change in any two positions in either picture above is always the same. In both cases you should find that the change is 20 m. This idea is true in a any situation. Regardless of where we place the reference point, the change in any two positions in either picture above is always the same. In both cases you should find that the change is 20 m. This idea is true in a any situation.

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

SCALARS SCALARS Scalars can be completely described by a magnitude value. Scalars can be completely described by a magnitude value. VECTORS VECTORS A vector quantity is described completely only if both its magnitude and direction are described

Scalar vrs. Vector Distance Distance 15 km15 km Speed Speed 30 m/s30 m/s Time Time 10s10s Mass Mass 6 kg6 kg Displacement Displacement 15 km [N 45 E] Velocity Velocity 30 m/s [S] Acceleration Acceleration 9.81 m/s [down]

Motion 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 possible to have a negative valueIndicates location of object from the reference point. It is possible to have a negative value Displacement Displacement Symbol: ΔdSymbol: Δd The distance from an initial position to the finishing positionThe distance from an initial position to the finishing position Δd = d f – d iΔd = d f – d i This change in position is actually given its own name. It is called the displacement. It is different than what we usually call distance. With distance we don't care where the reference point is but with displacement we do. This change in position is actually given its own name. It is called the displacement. It is different than what we usually call distance. With distance we don't care where the reference point is but with displacement we do.

Displacement and Velocity Diagrams allow you to describe motion qualitatively. We describe motion quantitatively by taking measurements Diagrams allow you to describe motion qualitatively. We describe motion quantitatively by taking measurements Two fundamental measurements involved in motion are distance and time. Using this you can calculate an object’s position, speed and rate of change of speed at any particular time Two fundamental measurements involved in motion are distance and time. Using this you can calculate an object’s position, speed and rate of change of speed at any particular time

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

Displacement Solution reference point: the starting point of the trip. This is why I've labelled the starting curb as x=0. The squirrel starts at the curb (x1) and 'finishes' at x2. We know that x1=0 since that is our zero line so we just need the value of x2. A little inspection should reveal that x2=5 m. The squirrel's displacement is then reference point: the starting point of the trip. This is why I've labelled the starting curb as x=0. The squirrel starts at the curb (x1) and 'finishes' at x2. We know that x1=0 since that is our zero line so we just need the value of x2. A little inspection should reveal that x2=5 m. The squirrel's displacement is then (No squirrels were harmed in the construction of this example.) (No squirrels were harmed in the construction of this example.)

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

Time and Time Intervals Time and Time Intervals The elapsed time between two instantsThe elapsed time between two instants Velocity Velocity Scalar - SpeedScalar - Speed Distance travelled divided by the time spent travelling Distance travelled divided by the time spent travelling Speed = distance /time Speed = 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 position Rate of change in position Average velocity = displacement /time Average velocity = displacement /time