Mechanics 1

  • Created by: S_F
  • Created on: 19-05-22 09:22
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  • Mechanics 1.0
    • Position vectors
      • x + s = new position vector
        • x = original position vector
        • s= displacement from x
      • For particles travelling at constant velocity, s=vt
      • s, u, a and v are all vectors while t is scalar. Vectors cannot be squared so V2 = u2 + (2as) cannot be used
    • Constant acceleration formulae in two dimensions
      • s = displacement in metres
      • u = initial velocity in metres per second
      • v = final velocity
        • At the object's maximum height, the vertical velocity is momentarily zero before it starts falling again
      • a = acceleration in metres per second squared
        • if an object is moving freely under gravity, the acceleration is just g
      • t = time
      • Modelling assumption: the object is a particle - its dimensions can be ignored and air resistance  does not act on it
    • Calculus in kinematics using vectors
      • If a particle is moving in a straight line with acceleration that varies with time, you need to use calculus
        • To find an equation for velocity, differentiate the equation for displacement with respect to time
        • To find an equation for a, differentiate the equation for velocity with respect to time
        • s -------------   v -------------  a -------------differentiate down and Integrate in the opposite way
    • Magnitude of a vector
      • The direction of a velocity vector gives the direction of motion of the object and the direction of its acceleration vector is the direction of the resultant force
      • speed is the magnitude of velocity - use Pythagoras' theorem
      • s = hi + vj direction: tan-1(v/h)
    • Projectile motion
      • Split velocity of projection into two components
        • A projectile with speed u at an angle to the horizontal has two components of initial velocity
          • horizontal: parallel to the x-axis
            • ucos(angle) - cosine cuts through the angle
          • vertical: usin(angle)
      • Split motion into horizontal and vertical components too
        • Deal with the vertical and horizontal components separately using the suvat equations.
        • The only thing that is the same in both directions is time - so this connects them
      • There is only vertical acceleration and due to gravity - horizontal acceleration is zero
      • velocity = zero at maximum velocity




This is specific to the advance information published for the June 2022 A level maths exams

Exam board: AQA

A brief summary of the main points for each topic

There will be another mechanics one and then 2 for statistics

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