2 Kinematics (AS)

2.1 Equations of motion:

2.1.1 Basic definitions:

  • Distance is the total path length traveled by an object and is a scalar quantity.
  • Displacement is the change in position of an object and includes both magnitude and direction, making it a vector quantity.
  • Speed is the rate at which an object covers distance and is calculated as the distance traveled divided by the time taken.
  • Velocity is the rate at which an object changes its displacement and is calculated as the displacement divided by the time taken.
  • Acceleration is the rate at which an object changes its velocity and is calculated as the change in velocity divided by the time taken.

2.1.2 Graphical representations:

  • Distance, displacement, speed, velocity, and acceleration can be represented graphically.
  • Distance and displacement are usually represented on position-time graphs.
  • Speed and velocity can be represented on speed-time or velocity-time graphs.
  • Acceleration is represented on acceleration-time graphs.

2.1.3 Displacement from the area under a velocity-time graph:

  • The displacement of an object can be determined by calculating the area under a velocity-time graph.
  • The area under the graph represents the change in displacement over a given time interval.

2.1.4 Velocity from the gradient of a displacement-time graph:

  • The velocity of an object can be determined by calculating the gradient (slope) of a displacement-time graph.
  • The gradient represents the rate of change of displacement with respect to time.

2.1.5 Acceleration from the gradient of a velocity-time graph:

  • The acceleration of an object can be determined by calculating the gradient of a velocity-time graph.
  • The gradient represents the rate of change of velocity with respect to time.

2.1.6 Equations for uniformly accelerated motion:

  • For uniformly accelerated motion in a straight line, the following equations can be derived from the definitions of velocity and acceleration:
    • v = u + at (final velocity = initial velocity + acceleration × time)
    • s = ut + (1/2)at² (displacement = initial velocity × time + (1/2)acceleration × time²)
    • v² = u² + 2as (final velocity² = initial velocity² + 2 × acceleration × displacement)
    • s = vt - (1/2)at² (displacement = final velocity × time - (1/2)acceleration × time²)

2.1.7 Motion in a uniform gravitational field:

  • Objects falling in a uniform gravitational field without air resistance experience uniformly accelerated motion.
  • The equations of motion for such objects can be used to analyze their motion.

2.1.8 Determining acceleration of free fall:

  • An experiment can be conducted to determine the acceleration of free fall using a falling object.
  • By measuring the time taken for the object to fall a known distance, the acceleration due to gravity can be calculated.

2.1.9 Motion with uniform velocity and uniform acceleration:

  • Motion can occur when an object has a uniform velocity in one direction and a uniform acceleration in a perpendicular direction.
  • The resulting motion can be described and explained by considering the independent effects of velocity and acceleration in different directions.