Physics Exam 1 Study Guide: Units, Motion, Vectors, and Problem Solving

Tips on Studying

Effective Exam Preparation Strategies

• Sample Exam Usage: Take the sample exam only after substantial studying. It is best used to identify any remaining gaps in your understanding, not as a primary study tool.

• Practice Under Test Conditions: When using the sample exam, simulate real test conditions (timed, with only allowed materials).

• Calculator Familiarity: Do not use a graphing calculator if not permitted. Practice with the allowed calculator to avoid surprises during the exam.

• Active Practice: Focus on solving problems rather than passive review. Work in groups, use practice problems, and review homework and lecture questions.

• Review Resources: Use lecture notes, pull questions, and practice problems for review.

• Problem Solving Approach: Do not rush to answer; spend time understanding the problem and planning your solution.

• Iterative Practice: Repeat problem-solving steps to reinforce learning. Avoid memorization; focus on understanding concepts.

• Rest: Ensure adequate sleep before the exam for optimal brain function.

Course Material Overview

Topics Covered

• Reading, homework, and workbook material for Chapters 1-3

• Warmups up to and including September 15

• Lecture points up to and including September 15

Exam Objectives

Units and Scientific Notation

Understanding units and scientific notation is fundamental in physics for expressing measurements and performing calculations.

• Unit Conversions: Convert between different units (e.g., cm2 to m2, mph to m/s, square meters to square kilometers).

• Example: Convert 27 cm2 to m2.

• SI Units and Derivatives: Recognize and use SI units (m, cm, km, kg, L, s, N, etc.) and relate them to everyday objects for estimation.

• Example: Estimate the mass of a typical smartphone in kg.

• Scientific and Decimal Notation: Convert numbers between scientific and decimal notation.

  • Example: Write 0.000225 in scientific notation: $2.25 \times 10^{-4}$

  • Example: Write $5.5 \times 10^{-7}$ in decimal notation: 0.00000055

Descriptions of Motion

Kinematic Quantities and Motion Analysis

Kinematics involves the study of motion without considering its causes. Key quantities include position, displacement, distance, velocity, speed, and acceleration.

• Position, Distance, and Displacement:

  • Position: Location of an object at a given time.

  • Distance: Total length of the path traveled (scalar).

  • Displacement: Change in position (vector).

  • Example: A particle moves from $x = 22$ cm to $x = -20$ cm. Displacement = $-42$ cm.

• Velocity and Speed:

  • Speed: Scalar quantity; rate of distance traveled.

  • Velocity: Vector quantity; rate of change of position.

  • Formula: $v = \frac{\Delta x}{\Delta t}$

  • Example: A car travels 400 m in 50.42 s. Average speed = $\frac{400}{50.42}$ m/s.

• Acceleration:

  • Definition: Rate of change of velocity.

  • Formula: $a = \frac{\Delta v}{\Delta t}$

  • Example: A car slows from 30 m/s to rest in 120 m. Find acceleration.

• Motion Diagrams: Visual representations of an object's position at successive times.

• Relating Verbal Descriptions and Diagrams: Match motion diagrams to physical scenarios (e.g., skater gliding, car braking).

• Motion Graphs: Interpret and relate position-time, velocity-time, and acceleration-time graphs.

  • Example: Identify which graph matches a given motion diagram.

Conceptual Analysis of Kinematic Situations

Multiple-Choice Reasoning

Conceptual questions test your understanding of kinematic principles and their application to real-world scenarios.

• Constant Velocity and Acceleration: Recognize situations with constant or changing velocity/acceleration.

• Example: An object moving at $-2$ m/s along the x-axis: travels 2 m in the negative direction every second.

• Projectile Motion: Analyze the motion of objects thrown into the air, considering maximum height and acceleration due to gravity ($g \approx 9.8$ m/s2).

• Example: At what point in a ball's flight is acceleration maximum? (Always $g$ downward, neglecting air resistance.)

Vectors

Graphical and Analytical Vector Operations

Vectors are quantities with both magnitude and direction, essential for describing physical phenomena such as displacement, velocity, and force.

• Vector Addition and Subtraction: Combine vectors graphically (tip-to-tail method) and analytically (component-wise).

• Example: Given vectors $\vec{A}$ and $\vec{B}$, determine the direction of $\vec{A} + \vec{B}$ or $\vec{A} - \vec{B}$.

• Vector Components: Resolve vectors into perpendicular components using trigonometry.

  • Formulas:

    • $A_x = A \cos \theta$

    • $A_y = A \sin \theta$

  • Example: A bird flies at 10 m/s at an angle of 40° above the x-axis. $v_x = 10 \cos 40^\circ$, $v_y = 10 \sin 40^\circ$.

• Adding/Subtracting Components: Add or subtract vector components to find resultant vectors.

• Example: Marquez walks 3 miles east, then 2 miles at 35° above due East. Find total displacement using components.

1D Motion Problems

Quantitative Problem Solving in One Dimension

These problems require using kinematic equations to solve for unknowns in linear motion.

• Kinematic Equations:

  • $v = v_0 + at$

  • $x = x_0 + v_0 t + \frac{1}{2} a t^2$

  • $v^2 = v_0^2 + 2a(x - x_0)$

• Example: A car travels at 60 mph for 2 hours. Distance = $60 \times 2 = 120$ miles.

• Example: A car decelerates from 20 m/s to rest in 2 seconds. $a = \frac{0 - 20}{2} = -10$ m/s2.

• Example: A ball is dropped from a building. Time to fall: $t = \sqrt{\frac{2h}{g}}$.

2D Motion Problems

Projectile and Circular Motion in Two Dimensions

These problems involve decomposing motion into x and y components, using kinematic equations, and analyzing projectile or circular motion.

• Projectile Motion: Analyze horizontal and vertical components separately.

  • Formulas:

    • Horizontal: $x = v_{0x} t$

    • Vertical: $y = v_{0y} t - \frac{1}{2} g t^2$

  • Example: A helicopter drops a package horizontally at 40 m/s. How far does it travel in 5 seconds? $x = 40 \times 5 = 200$ m.

  • Example: A ball is kicked from ground level at 15 m/s at 30°. Find time to hit the ground and horizontal distance.

• Circular Motion: Use equations for uniform circular motion.

  • Formula: Centripetal acceleration: $a_c = \frac{v^2}{r}$

  • Example: A pilot flying in a circle of radius 200 m at 900 m/s. $a_c = \frac{900^2}{200}$

Summary Table: Kinematic Quantities

Quantity	Symbol	Definition	SI Unit
Position	x	Location of object	m
Displacement	Δx	Change in position	m
Distance	d	Total path length	m
Speed	v	Rate of distance traveled	m/s
Velocity	v	Rate of change of position	m/s
Acceleration	a	Rate of change of velocity	m/s2

Additional info:

• Students should be familiar with interpreting motion diagrams and graphs, as well as translating between verbal, graphical, and mathematical descriptions of motion.

• Practice problems and conceptual questions are essential for mastering these topics.