Unit 1 · 1.2 — Displacement, Velocity, and Acceleration

Everything to learn here

• Concept: Speed is the scalar rate of distance traveled; velocity is the vector rate of displacement
• Concept: Average velocity is the rate of change of position over a time interval; instantaneous velocity is the velocity at a specific moment in time
• Concept: Acceleration is the vector rate of change of velocity; it occurs when an object changes speed, changes direction, or both
• Concept: If velocity and acceleration vectors point in the same direction (same sign), the object speeds up; if they point in opposite directions (opposite signs), it slows down
• Concept: A negative acceleration does not inherently mean an object is slowing down; it simply means the acceleration vector points in the negative direction
• Concept: Uniform acceleration allows the use of the constant acceleration kinematic equations (the "Big Five")
• Equation: $$S=\frac{d}{t}\text{(Average Speed)}$$
• Equation: $$v_{avg}=\Delta x/\Delta t\text{(Average Velocity)}$$
• Equation: $$a_{avg}=\Delta v/\Delta t\text{(Average Acceleration)}$$
• Equation: $$v_x=v_{x0}+a_x\cdot t\text{(Kinematic Equation 1: Velocity as a function of time)}$$
• Equation: $$x=x_0+v_{x0}\cdot t+0.5\cdot a_x\cdot t^2\text{(Kinematic Equation 2: Position as a function of time)}$$
• Equation: $$v_x^2=v_{x0}^2+2\cdot a_x\cdot (x-x_0)\text{(Kinematic Equation 3: Velocity as a function of position)}$$
• Equation: $$\Delta x=0.5\cdot (v_0+v)\cdot t\text{(Kinematic Equation 4: Displacement using average velocity)}$$
• Vocabulary: Velocity — The rate of change of displacement with respect to time
• Vocabulary: Acceleration — The rate of change of velocity with respect to time
• Vocabulary: Free Fall — A state of motion where the only force acting on an object is gravity, resulting in a constant downward acceleration (g = 9.8 m/s^2)
• Skill: Mathematical Routines — Selecting the correct kinematic equation based on knowns and unknowns, recognizing they apply strictly when acceleration is constant
• Skill: Experimental Design — Use a motion sensor or photogate to collect continuous position and time data to calculate empirical velocity and acceleration
• Skill: Common Error Avoidance — Do not substitute average velocity into equations requiring instantaneous initial or final velocity
• Concept: In the object model, an object's size, shape, and internal configuration are ignored — the object is treated as a single point with only external interactions considered
• Concept: Calculating average velocity or average acceleration over a very small time interval yields a value very close to the instantaneous velocity or acceleration at that moment
• Equation: $$a=\Delta v/\Delta t;averageaccelerationisthechangeinvelocitydividedbythetimeintervalofthatchange.$$

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