Module 3 1D & 2D Kinematics (13 Days)
Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Kinematics is a branch of mechanics. The goal of any study of kinematics is to develop sophisticated mental models that serve to describe (and ultimately, explain) the motion of real-world objects.
In the last unit, the student gained experience with motion through measurements and graphical techniques. That motion was limited to one dimension and the emphasis was on graphing techniques and interpretation of the graphs.
In this unit, the emphasis is again on motion, but in addition to taking measurements and graphing the motion, the student will be expected to perform calculations involving the motion variables. Basic kinematics problems with constant acceleration are important in their own right but are also used to develop problem-solving skills.
As the motion moves from one to two dimensions, the concepts of vectors become important. The student will learn to represent the vector quantities of velocity, acceleration, and displacement with vectors. With these skills, the variables of projectile motion (an important 2D problem) will be resolved. The motion investigated to date is translational or linear motion of a point object. Problems involving uniform circular motion of a point and rotation of a circular object are introduced with similar equations of motion.
How can the motion of an object be described using more than just words?
How can mathematics be used to describe the motion of an object in a precise manner?
If we can measure certain dimensions of an object's motion, can we predict other unknown dimensions accurately?
How can an observer describe the motion of an object in one or two dimension using such quantities as position, displacement, distance, velocity, speed and acceleration?
Is this video real or faked? Can Kinematics help us decide?
Knowledge & Skills
Describe and analyze motion in one dimension using equations with the concepts of distance, displacement, speed, average velocity, instantaneous velocity, and acceleration.
The students will be able to describe and analyze motion in one dimension using equations including, but not limited to:
Vectors vs scalars
Vector quantities of displacement and vector sum
a2 + b2 = c2
Displacement = (initial velocity)(change in time) + ½ (acceleration)(change in time)2
Δd = viΔt + ½aΔt2
Average velocity = displacement/change in time
vavg = Δd/Δt
Acceleration = final velocity – initial velocity/change in time
a = vf – vi /Δt
Acceleration = (final velocity)2 – (initial velocity)2/2(displacement)
a = vf2 – vi2/2Δd
The students will analyze and describe accelerated motion in two dimensions using equations, including projectile and circular examples.
Including, but not limited to:
Centripetal acceleration = (tangential velocity)2/radius
ac = vt2/r
Torque = (force)(lever arm)
Acceleration problems involving uniform acceleration and free fall using the kinematic equations
The motion of objects can be described by words. Even a person without a background in physics has a collection of words that can be used to describe moving objects. In this unit students will understand how to describe the motion of objects using mathematical equations.
In two dimensional motion, displacement, velocity, and acceleration must be treated as vector quantities. The magnitude angle and component forms of vectors are used in studying these motions.
What are vectors?
What are the vector quantities describing motion?
What are the basic equations describing linear motion?
How are basic kinematics equations used to describe projectile motion?
Students may think that acceleration and velocity are always in the same direction.
Students may think that an object thrown into the air has zero acceleration at the highest point.
Students may think that velocity is a force.
Students may think contant motion requires a constant force.
Sttudents may think if an object is accelerating, then it is speeding up.
Students may think the distance an object travels and its displacement are always the same.
Kinematics – the study of how things move
Vector – physical quantity that has both a magnitude and a direction
Scalar – specified numbers or units on a scale
Velocity – vector quantity that measures rate of change of position of an object
Graphically represent and analyze a problem situation related to projectile motion. Complete a laboratory report that includes the proper use of significant figures and error analysis.
This module will have a performance indicator as well as the unit assessment and one exam.