### Online Geometry Class and Physics Problems: Motion in One and Two Dimensions

Learning Target 2.1 – 2.5 = 1 Hr 2.1 Describe average velocity and basic circumstances when it may be positive or negative.
• L uses Fig. 2.1 and Fig 2.2 to discuss the difference between +x and -x. Defines displacement and ask.
• Q (1) How would you describe average velocity based on the figures?
• L reacts to the answer of students
• Q (2) In which of the figures is average velocity positive and negative?
• L reacts to the answers and clarifies the concept of average velocity.
2.2 Apply the concept of average velocity to solve exercises involving distance covered by a body and time of trip
• L gives example using Ex. 2-1 integrating the problem-solving strategy given in p.44
• T solve Ex. 2-3 and Ex. 2-4.
• L moves around and check student’s work, then gives a brief discussion to the solution of 2-4 (Note: Ex. 2-3 may no longer be discussed especially if most students get the answer)
2.3 Define speed and differentiate it from velocity
• L refers to the speedometer of a car and ask a question
• Q (1) Does the speedometer of a car measure speed or velocity?
• Q (2) Does the speedometer gives an information on where the car is heading?”
(2) No, only an information of the magnitude.
• L reacts and clarifies the differences between velocity and speed.
2.4 Solve an exercise involving both speed and velocity
• T solve Ex. 2-6
• L moves around and interacts with students. May discuss the solution of the exercise.
2.5 Defines vins mathematically and differentiate it from vav
L discusses Fig 2.5 (a,b,c)
Q From Fig. 2.5c, what is the mathematical definition of vins ? How can you differentiate it from vave+?
Answer: vins=dx/dt. The average velocity does not give information on how fast and in what direction a body moves at a specific instant unlike the instantaneous velocity.
• L reacts to the answer and explains further that for a straight- line graph vins= vave
2.6 Apply the definition of vins in a curve of an x-t graph to solve an exercise
• L discusses Fig. 2-6 emphasizing the concept of the slope of the tangent line to a curve
Horizontal (v is zero)
Slanting to the left (v is negative)
So slanting to the left (v is negative with large magnitude)
Slanting to the right (v is positive)
So slanting to the right (v is positive with large magnitude)
• T solve Ex. 2-8
• L moves around and checks the solution of the students. May discuss the solution.
2.7 a) Define mathematically aave and ains and differentiate them
b) then solve two exercises on these concepts. • L discusses aave and ains based on the v-t graph of Fig. 2-9
(Note: Emphasizes that as P2 approaches P1 aave = ains. Recalls vave and vins)
• Q asks for the equations of aave and ains based on the discussion
• L reacts and writes the equations on the board
• L discusses Example 2-3
• T solve Ex. 2-10 and Ex. 2-11 (a,b,c,d)
• L move around and check the solution of the student and interact with the students. Discusses Ex. 2-10. May or may not discuss Ex. 2-11.
pp.53-54
2.8 Interpret the concept of motion with constant acceleration (UALM) by graphing • L explains UALM based on Figs. 2-12, 2-13, 2-14. Emphasizes that there is a constant increase or decrease in speed for every second of the motion of the body.
• T determine the speed of a body every second if it is moving in a straight line having an initial speed of zero and acceleration a= 2.0 m/s2 . Then plot a v-t graph based on these values given the following
• L moves around and interacts with the students p. 41
2.9 Use the five equations to solve problems related to UALM • L writes the defined equations: vave, a, and stat. vave. You may or may not derive the other 2 equations.
• L explains Example 2-4 and Example 2-5 and incorporates the problem-solving strategy
• T Half of students solve Ex. 2-21 and half solve Ex. 2-23. Two adjacent rows can move closer and discuss by two’s
• L discusses only one exercise
• Assignment: Solve Ex. 2-58 and Ex. 2-59
• L writes the solution in a Manila paper for students to compare their answers for the following meeting
2.10 Transform the five equations of UALM into 5 equations for freely falling body.
• L Explain the kinematics of a freely falling body
• T students write down the 5 eqns. for a free fall. This should be done to show that a freely falling body is UALM
• T Let the student describe about the distances the object has fallen for every second. Then asks the students whether v is constant or not. Why or why not?
• L reacts to the answer and emphasizes that the displacement of a falling body is increasing in the negative direction and decreasing in the positive direction with time
2.11 Apply the concept of freely falling body to solve exercises on finding the highest point reached and the velocity every second of fall
• L discusses Example 2-6 and Example 2-7
• T solve Ex. 2-38 and Ex. 2-39
• L reacts to the answer. Discusses only Ex. 2-38.
• L gives a quiz from the handout
• Assignment: Solve Ex. 2-66 and Ex. 2-67
• L writes the answer in a Manila paper for students to compare.
2.12 Use the concepts to explain questions related to real-life situation • Q (1) Charlie drove his car around a block at constant velocity. True or false? Why?
• L reacts to the answers
Answer: false. The velocity can not be constant because there would be a change in direction as the car rounds a block.
• Q (2) Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its speed increases with each second of fall?
• L reacts to the answers
Answer: every second there is an increase in speed by 9.8 m/s.
• Q (3) Someone standing at the edge of a cliff throws a ball straight up at a certain speed and another ball straight down with the same speed. Compare their speed when they hit the ground, if air resistance is neglected. Answer: the same speed.
2.13 Predict and describe the time of fall of the two coins from the bamboo launcher • L describes an activity to the students using the bamboo launcher and two coins
• Q predict on the time of fall of the of the two coins
• L does the activity and illustrate the result of the activity Demo with H4
2.14 Describe the x- and y- motion of the projectile projected horizontally and a projectile projected at a certain angle
• L explains the kinematics of a body projected horizontally and a body projected at a certain angle based on Sec 3-4 and Fig. 3-14 (using shadow effects in the x- and y-axes of the projectile)
• Q Describe the velocity and acceleration of the projectile along the x- and y-axes.
Answer: the x-velocity is constant in magnitude and direction while the y-velocity follows that of a freely falling body. Acceleration is constant is constant and is equal to g.
• L reacts and emphasizes the magnitude and direction of the x- and y- velocities.
2.15 Use the concepts to calculate time of fall, highest point reached, horizontal displacement, etc. • L writes down the UALM equations of a projectile projected horizontally (Note: you may derive the different quantities such as time of flight, highest point reached, velocity, etc)
• L discusses Example 3-6
• T solve Ex. 3-10 and Ex. 3-11 in groups of two or three students
(Alternate exercises: from handout)
• L moves around and check solutions. Discusses Ex. 3-10.
• Assignment: Solve Prob. 3-49 and Prob. 3-50
• L writes the answer in a Manila paper for students to compare their answers for the following meeting L reacts to the answers by asking students to write down on the board
2.17 Describe the motion of a projectile projected at a certain angle that starts and ends or passes through the origin and then solve an exercise related to this motion • L discusses Fig. 3-15 and the equations highlighted and presented in
• L discusses Example 3-7
• T solve Ex. 3-14 and Ex. 3-15 in groups of 3 or 4 students
(Alternate exercise is from the handout)
• L moves around and checks students’ solutions ,
discusses Ex. 3-14
• Assignment: Solve Ex. 3-55 and Ex. 3-57
• L writes the answer in a Manila paper for students to compare their answers for the following meeting
2.18 Describe the motion of a body moving in a uniform circular motion and calculate the velocity and radial acceleration of the body at a particular point of its path.
• L explains UCM based on Sec 3-5
• Q Describe the motion of a body moving in a circular motion
Answer: the magnitude of the velocity of the body is constant but its direction is changing (tangent to the point of the path where the body is located). The centripetal acceleration is directed toward the center. There is no tangential acceleration because there is no change in speed.
• L reacts and emphasize that the acceleration is always perpendicular to the direction of the velocity p. 76
2.19 Calculate velocity and radial acceleration using the equations for UCM • L discusses Example 3-11 and Example 3-12
• T Solve Ex. 3-23 individually
• L moves around and interacts with the students