# Dimensions, Vectors, and Kinematics LGs: Sp14

I’m teaching calculus-based Physics 1 for the first time this semester. Actually, Calc I is a co-requisit not a prerequisite for this class so I’ll show students some calculus but they won’t do much themselves until Physics 2. Anyway, here is my current set of learning goals for Unit 1.

**Content Learning Goals**

Upon successful completion of this unit the student will be able to…

1. Recognize the power of 10 associated with the prefixes: nano, micro, milli, centi, kilo, mega, giga. The student can move fluently between numerical powers of 10 (i.e. 10^{-3}) and prefixes (i.e. milli) in conversation and in written problems.

2. Recall the S.I. units for length, time, speed, acceleration, and mass. The student also knows how various algebraic operations affect units and can use this knowledge to keep track of units while solving problems.

3. Recall approximate (order of magnitude) values in meters and kilograms for: the height of an adult, the mass of an adult, the length of a football field, the length of a mile, and the mass of a car. The student can also recall approximate values in meters per second for: a person running, a car driving, a plane flying. The student can use these values to solve estimation problems and to assess the reasonableness of his or her answers to various problems.

4. Determine when dimensions must match and when they need not match when combining terms. The student can explain the meaning of the phrase ‘dimensional analysis’ and can use dimensional analysis to assess the appropriateness of new equations and to construct approximate equations for order of magnitude problems.

5. Explain the difference between velocity and acceleration and can give examples of motion in which: one quantity is zero and the other is non-zero, one quantity is positive and the other is negative, each quantity points in a different direction. The student can also explain the meaning of the phrase ‘rate of change’.

6. Explain the difference between a vector and a scalar and classify common quantities such as position, distance, displacement, speed, velocity, acceleration, mass, and density as scalars or vectors.

7. Differentiate between instantaneous and average values for speed, velocity, and acceleration. The student can calculate instantaneous and/or average quantities given: a table of values, a graph, a description of motion in words, or a kinematic equation. The student can also explain under what types of motion the average and instantaneous value of a quantity will be the same.

8. Recall equations v = v_{0} + at, v^{2} = v_{0}^{2} + 2ad, <v> = (v + v_{0})/2, and x = x_{0} + v_{0}t + 1/2at^{2}. The student can explain under what conditions these equations are valid and can use them to setup and solve kinematics problems.

9. Translate between different ways of representing motion: description in words, x vs. t or v vs. t graphs, equations, and motion maps. Given any representation, the student can construct any of the other representations. The student can also explain when each representation might be useful.

10. Define ‘free fall’ and explain what free fall implies and does not imply about the values of kinematic quantities v_{0}, v, and a.

11. Explain the meaning of the magnitude of a vector and the meaning of symbols \vec{*A*}, |\vec{*A*}|, and *A *for a general vector. The student can also calculate the magnitude of a one-, two-, or three dimensional vector.

12. Draw a right triangle for any 2D vector and use SohCahToa to determine the components of the vector.

13. Add or subtract two or more vectors both graphically (for 1D or 2D) and algebraically (for 1D, 2D, or 3D) and give the results in cartesian or polar coordinates. The student should be able to do this regardless of whether the original vectors are given in cartesian or polar coordinates. The student can also multiple a vector by a scalar both graphically and algebraically.

14. Explain the meaning of unit vector and recall how unit vectors are denoted. The student can recall how i-hat, j-hat, and k-hat relate to the x, y, and z axes. Given a vector , the student can represent this vector in either (A_{x}, A_{y}, A_{z}) notation or in A_{x} i-hat + A_{y} j-hat + A_{z} k-hat notation.

15. Determine the value and direction of velocity and acceleration for an object thrown straight up when the object is: in the hand being thrown, halfway to the top, at the very top, halfway down, in the hand being caught.

16. Solve 2D kinematics problems by separating the motion into horizontal and vertical components and applying our basic kinematics equations (LG 8) to each component individually.

17. Define ‘projectile motion’ and solve for maximum height, horizontal distance, and time of flight for a projectile. The student can also calculate horizontal or vertical position, displacement, velocity, and acceleration at any moment during the projectile’s flight.

I’ve not written General Skills or Experiential learning goals for this unit.