Kinematics

Kinematics

Unit 1: Motion Pt 1

Date: Thursday, 15 August 2024

Key Questions

  • How can the motion of a body be described?

    • Quantitatively (using measurements) and qualitatively (using descriptions).

  • How can an object's position in space and time be predicted?

  • How can the analysis of one and two-dimensional motion solve real-life problems?

Review of IGCSE

The initial concepts will align with IGCSE, understanding past knowledge is crucial as it builds the basis for the IB course.

Vectors and Scalars

  • Scalar: A quantity with magnitude but no direction.

    • Examples: Speed, distance, temperature.

  • Vector: A quantity with both magnitude and direction.

    • Examples: Force, velocity, momentum.Direction includes angles and must be considered in more depth than at IGCSE.

Worked Examples

  • Example 1: Ball DropA ball dropped from a height of 1.2m:

    • Maximum Height After Bounce:

      • Height after rebound = 0.75 × 1.2m = 0.9m.

    • Displacement = 0.9m - 0 = 0.9m.

    • Total distance traveled = 1.2m + 0.9m = 2.1m.

  • Example 2: Cyclist MovementCyclist travels 250m up a slope at an angle of 8°.

    • Change in Height:

      • Height = 250 * sin(8°) ≈ 35m.

    • Horizontal Component:

      • Horizontal distance = 250 * cos(8°) ≈ 248m.

Speed and Velocity

  • Speed: Scalar quantity; Velocity: Vector quantity.

  • Formula: V = D/t

    • Example: A train travels at 280 km/h, length calculation based on speed and time needs to be completed as per the example.

Worked Example: Train

  • Train passing a pole at 280km/h (constant speed):

    • Convert speed to m/s:

      • 280 km/h = 77.8 m/s.

    • Time to pass a pole (2.3s):

      • Length of train = 77.8 m/s * 2.3s = 180m.

Graphs of Motion

Graphs illustrate speed and distance over time:

  • Steeper gradient = faster motion; Flat line = stopped.

  • Negative gradient indicates return to start.

Instantaneous vs Average Speed

  • Instantaneous speed is a more accurate description of motion, capturing speed at any moment.

  • Average speed is used for general measurements over time.

Worked Example: Distance Graph

Calculating instantaneous speed at specific times requires reading values directly from the graph.

SUVAT Equations

Used for motions with constant acceleration:Complete the equation table linking displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).Equations of motion include:

  • v = u + at

  • s = ut + 1/2 at²

  • v² = u² + 2as

Projectile Motion

Analyzing this involves considering vertical and horizontal components separately.

  • Worked Example 1: Dropping an Object

    • Calculate time from drop, velocity upon hitting water, and total height of a well.

  • Worked Example 2: Hot Air Balloon

    • Object released from a rising balloon and how it reaches the ground while accounting for gravitational effects.

Moving Through Fluids

Discuss important implications of air resistance on motion, both in one and two dimensions.

  • Example of a projectile's trajectory changes due to air resistance compared to ideal calculations.

Summary of Air Resistance Effects

Overall, air resistance causes increases in fall time, and changes in acceleration and distance traveled compared to calculations without it.