(455) Uniformly accelerated motion 1 [IB Physics SL/HL]

Introduction to Uniformly Accelerated Motion

  • Uniformly accelerated motion is fundamental in physics.

  • Understanding its principles is crucial for grasping more complex concepts.

Motion Without Acceleration

  • When not accelerating, equations of motion simplify:

    • Velocity (V) = Distance (S) / Time (T)

    • Example: If S = 100 m and T = 5 s, then V = 100 m / 5 s = 20 m/s.

Key Concepts in Accelerated Motion

  • Four main equations of motion to understand:

    1. V = U + A T (Final velocity = Initial velocity + Acceleration × Time)

    2. S = U T + 1/2 A T² (Displacement = Initial velocity × Time + 1/2 × Acceleration × Time²)

    3. V² = U² + 2 A S (Final velocity² = Initial velocity² + 2 × Acceleration × Displacement)

    4. S = (V + U) * T / 2 (Displacement = Average velocity × Time)

  • Acceleration (A) is defined as change in velocity over change in time.

Variables in Equations

  • Important variables:

    • S = Displacement (meters);

    • U = Initial velocity (meters/second);

    • V = Final velocity (meters/second);

    • A = Acceleration (meters/second²);

    • T = Time (seconds).

  • Time is a scalar quantity; velocity and displacement are vectors.

Understanding Velocity

  • Velocity is the rate of change of displacement:

    • Formula: Velocity = Change in displacement / Change in time.

    • Graphical interpretation: Slope of the displacement vs. time graph represents velocity.

Acceleration and Units

  • Acceleration is the rate of change of velocity:

    • Units: meters/second² (m/s²).

    • Relationship: If velocity (V) has units of m/s, then acceleration will be m/s² when divided by time (seconds).

Solving Accelerated Motion Problems

  • Use the method UAT (or SUAT) as a checklist:

    • List known values for U, V, A, S, T, marking unknowns.

    • Ensure units are consistent (e.g., convert cm to m).

Example Problem

  • Situation: Driving a car with initial speed (U) of 21 m/s and decelerating at -3.2 m/s².

    • Find time (T) to stop (V = 0):

    • Given: U = 21 m/s, A = -3.2 m/s².

    • Choose equation: V = U + A T.

    • Rearrange: T = (V - U) / A = (0 - 21) / -3.2.

    • Calculate: T = 21 m/s / 3.2 m/s² = 6.5625 seconds.

    • Final result: T ≈ 6.6 seconds.