Kinematics OCR A Level Physics

Kinematics in Physics

Definitions of Key Concepts

  • Scalar Quantities

    • Only have magnitude (size)
    • Examples:
    • Distance: Total length between two points
    • Speed: Total distance travelled per unit of time

  • Vector Quantities

    • Have both magnitude and direction
    • Examples:
    • Displacement: Distance from a fixed point in a specific direction
    • Velocity: Rate of change of displacement
    • Acceleration: Rate of change of velocity

Equations for Velocity & Acceleration

  • Relevant equations linking displacement, velocity, and acceleration are key understanding areas:
    • For calculating average velocity:
      v_{avg} = \frac{\Delta x}{\Delta t}
      where ( \Delta x ) is the change in displacement and ( \Delta t ) is the change in time.

Instantaneous Speed/Velocity

  • Definition: Speed (or velocity) at any given point in time.
  • For accelerating objects:
    • Represented by a curved line on a displacement-time graph
  • To find instantaneous velocity:
    1. Draw a tangent at the required time on the graph
    2. Calculate the gradient of that tangent.
  • Example: A car accelerates from rest to a speed of 150 km/h in 6.2 s.
    • Calculate the acceleration in m/s².

Average Speed/Velocity

  • Definition: Total distance (or displacement) divided by total time.
  • To find average velocity on a displacement-time graph:
    v_{avg} = \frac{\text{total displacement}}{\text{total time}}
  • Worked Example:
    • Cyclist travels 20 m then decelerates to a stop 5 m ahead in 3.5 s.
    • Total distance = 20 m + 5 m = 25 m
    • Average speed:
      v_{avg} = \frac{25 m}{3.5 s} = 7.14 m/s

Motion Graphs

  • Three types of motion graphs:
    • Displacement-Time Graphs
    • Velocity-Time Graphs
    • Acceleration-Time Graphs
Displacement-Time Graphs
  • Gradient (slope) = velocity
  • Y-intercept = initial displacement
  • Key features:
    • Diagonal line = constant velocity
    • Positive slope = positive direction; negative slope = negative direction
    • Curved line = acceleration; horizontal line = state of rest.
Velocity-Time Graphs
  • Gradient (slope) = acceleration
  • Y-intercept = initial velocity
  • Key features:
    • Straight line = uniform acceleration
    • Positive slope = increasing velocity; negative slope = decreasing velocity
    • Area under the curve = displacement.
Acceleration-Time Graphs
  • Gradient = meaningless
  • Y-intercept = initial acceleration
  • Area under the curve = change in velocity.

Displacement & Velocity-Time Graphs

  • Displacement-Time: Show changing position, can identify motion direction (positive/negative).

  • Velocity-Time: Illustrate speed and direction over time.

    • Area under graph = displacement.
    • Acceleration relates to changes in velocity, including direction.

Example of Motion (Bouncing Ball)

  • In a uniform gravitational field:
    • Positive velocity when moving upwards; negative when moving downwards.
    • At highest point (A): Zero velocity, maximum displacement.
    • At lowest point (B): Instantaneous change in velocity from negative to positive, but speed remains constant.

Summary of Gradients & Areas

  • Gradient of:
    • Displacement-Time Graph = Velocity
    • Velocity-Time Graph = Acceleration
  • Area Under:
    • Velocity-Time Graph = Displacement
    • Acceleration-Time Graph = Velocity

Examiner Tips and Tricks

  • Always double-check y-axis values on motion graphs to avoid confusion.
  • Ensure comfort with calculating areas, breaking graphs into manageable shapes (triangles, squares, rectangles).