Kinematics

Kinematics-What is it? Kinematics is the study of motion. –Motion is always defined in terms of change in location.  Locations or Positions are defined in terms of some FRAME of REFERENCE (F/R). –Many times we use our bodies or other objects to define F/R. –: – Vector Quantity –

Scalars and Vectors When discussing kinematics, and truly, all aspects of physics, we will be using two different types of measurements –Scalar Quantity: Scalar Quantities tell about Magnitudes (how much or how big.) The Price is $12.00 is a scalar. –Vectors have magnitudes, but they also tell us about the Direction of the magnitude. The price Increased by $12.00 is a Vector.

Vectors As stated, a vector is a magnitude (How big or How much) with a direction. Often we will draw vectors as arrows pointing in the direction of the vector. We can add vectors (vector addition): –Algebraically by placing the vectors head to tail and then finding the algebraic sum –or Graphically. ( x or y)

Adding Vectors We will do an entire unit with vectors at a later date!

Distance is a Scalar Distance and Displacement seem very similar, but they actually have distinct meanings. –Distance is a scalar quantity which refers to how far a body moves in going from one point to another. EX: 12 m is a distance…it tells how far.

Displacement is a Vector Displacement (generally written as…. Δx or Δ y…..is a vector quantity which refers to the distance between two points in a particular direction. Direction can be given in a lot of ways, by compass directions (N, S, E, W) or by + or – sign along the x (Δx = x f - x i ) or y (Δ y = y f - y i ) axis.

Example #1 A student walks 100 m to the East and then walks 300 m to the West. –What is the student’s total distance traveled? –At the end of her walk, what is her total displacement?

Example #2 A student walks 4 m east, 2 m south, 4 m west, and finally 2 m north. –What is the students total distance? Displacement?

Example #3 A family travels 50 km south on I-75 and then gets off on exit 117 and follows a dirt road 15 km east. –What is the families total distance traveled? – At the end of their trip, what is their total displacement?

Speed & Velocity Speed – It’s a scalar (v) Velocity – It’s a vector

Calculating Speed In order to find the average speed or average magnitude of an objects velocity divide the distance it has traveled by the time it took to travel that distance. –Speed = distance/time. –S = d/t S= d / t

Defining and Calculating Velocity We can look at and velocity in a couple of ways –Instantaneous velocity – This is what a speedometer gives you….how fast you’re going at a particular instant. –Average velocity – The average of all of the instantaneous speeds for a trip.. This is what we will deal with almost all of the time.

Calculating Velocity Velocity is It’s important to remember that Displacement has Direction!

Practice 1.What is the velocity of a car that travels 75 km towards Richmond in 5/6 hour (give answer in km/hr and m/s) 2.What is the speed of a person who runs 10 km in 1.5 hours (answer in km/hr and m/s)

Acceleration Acceleration is the measure of how velocity changes over a particular length of time.

More Acceleration Acceleration is a measure of how velocity (a vector) changes during a particular length of time. Remember! Vectors not only tell How Big a Quantity is, but also in What Direction that Quantity Acts. So, a body may travel at a constant speed, but IF IT CHANGES DIRECTION, it is ACCELERATING!!!

Centripetal Acceleration An object moving in a circle is accelerating because it’s direction is changing even if it’s speed is remaining constant

Acceleration is a VECTOR This means that Acceleration has a Magnitude (How Big the Change in Velocity is) It also tells us in what Direction that Change in Velocity takes place. This is normally done with + or – signs. + means to the right or up - means to the left or down

More Acceleration So by convention, if an object is speeding up, and the acceleration (speeding up) is in the same direction as the velocity. This gives the object a positive acceleration. If an object is slowing down, and the acceleration (slowing down) is in the opposite direction of the velocity. This gives the object a negative acceleration.

Examples of acceleration –Give some examples of positive acceleration –Give some examples of negative acceleration Name four controls in a car that can cause an acceleration

Calculating acceleration To find acceleration, we divide the change in velocity by the time it takes for that change (rate of change of velocity) Acceleration = change in velocity/time

Practice Problems 1.A vehicle initially traveling westward at 35 km/hr and comes to a stop in 15 s. What is the magnitude and direction of the acceleration of the vehicle? 2.A rock is dropped from the top of a cliff and after 10 seconds is traveling 40 m/s. What is the magnitude and direction of the rock’s acceleration?