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).