Recording-2025-02-07T18:28:26.138Z

Introduction to Acceleration in Two Dimensions

• Focus on acceleration when objects change direction.

• Previously studied acceleration in a linear motion; this year, we'll study more complex movements.

Definition of Acceleration

• Defined as: ( a = \frac{\Delta v}{\Delta t} )

  • ( \Delta v ): Change in velocity

  • ( \Delta t ): Change in time

• The Greek letter delta (( \Delta )) signifies "change in" in scientific contexts.

• Rewrite acceleration equation:

  • Final velocity (v)

  • Initial velocity (v₀) (sometimes written as v-naught)

  • Time (t)

• Usually, we measure velocities in ( m/s ) or ( km/h ).

Units of Acceleration

• Example from previous class: ( a = \frac{v - v₀}{t} )

• Emphasis on understanding consistent letters in physics terminology across high school and university.

Formula Sheet Guidelines

• Students allowed to create their own formula sheets for tests and exams.

  • Must only contain formulas; no notes or sample problems.

  • Encourages students to familiarize themselves with the material.

• Tips for making a formula sheet

  • Include all relevant formulas from the entire year.

  • Use both sides of the sheet for space.

  • Consider letter conventions in the physics community.

Transitioning to 2D Problems

• Moving from 1D to 2D increases complexity significantly.

• We will focus on vector subtraction in cases where directions change.

Example Problem 1: Car's Acceleration

• Scenario: Brooke drives around a corner, initially going 72 km/h east, then 72 km/h south in 2 seconds.

• Key point: Simply subtracting velocities (( 72 - 72 )) leads to incorrect assumptions; we must handle vector subtraction.

• Steps:

  1. Identify initial velocity (v₀): 72 km/h east.

  2. Identify final velocity (v): 72 km/h south.

  3. Draw a coordinate system for visualization.

  4. Perform vector subtraction using initial and final velocities.- Recognize the correct approach for finding the change in velocity (( \Delta v )).

• Resulting acceleration calculated: 51 km/h/s southwest.

Example Problem 2: Soccer Ball's Acceleration

• Scenario: A soccer ball moving at 15 m/s north 30° west, strikes the goalpost, and exits at 14 m/s north 30° east for 0.1 seconds.

• Reiterate importance of visual representation of vectors.

• Steps:

  1. Draw initial velocity (v₀) and final velocity (v).

  2. Use vector subtraction according to coordinate direction.

  3. Identify angles and utilize sine and cosine laws for calculations.

• Resulting acceleration will indicate direction, incorporating lessons from previous example.