Kinematics

• Distance


  A measure of how far an object travels. It is a scalar quantity - the direction is not important.
• Displacement


  A measure of how far something is from its starting position, along with its direction. It is a vector quantity - it describes both magnitude and direction.
• Distance is a scalar quantity because it describes how far an object has travelled overall, but not the direction it has travelled in.
• Displacement is a vector quantity because it describes how far an object is from where it started and in what direction.
• The difference between distance and displacement is that distance is a scalar while displacement is a vector.
• Speed


  The distance an object travels every second. It is a scalar quantity.
• Velocity


  The rate of change of position. It is a vector quantity because it describes both magnitude and direction.
• The difference between speed and velocity is that speed is a scalar quantity while velocity is a vector quantity.
• Instantaneous speed/velocity


  The speed/velocity of an object at any given point in time.
• Average speed/velocity


  The total distance/displacement divided by the total time taken.
• Acceleration is the rate of change of velocity. It is a vector quantity.
• Negative acceleration is called deceleration.
• Kinematic equations


  A set of four equations that can describe any object moving with constant or uniform acceleration, relating displacement, initial velocity, final velocity, acceleration, and time.
• Deriving kinematic equations


  Using calculus to derive the four kinematic equations from the definitions of velocity and acceleration.
• Key things to look out for when using kinematic equations are 'starts from rest', 'falling due to gravity', and 'constant acceleration in a straight line'.
• Starts from rest


  This means u = 0 and t = 0
• Falling due to gravity


  This means a = g = 9.81 m/s^2
• It doesn't matter which way is positive or negative for the scenario, as long as it is consistent for all the vector quantities
• If downwards is considered positive, this is 9.81 m/s^2, otherwise, it is -9.81 m/s^2
• For example, if downwards is negative then for a ball travelling upwards, s must be positive and a must be negative
• Constant acceleration in a straight line


  This is a key indication for the kinematic equations are intended to be used
• For example, an object falling in a uniform gravitational field without air resistance
• How to use the kinematic formulae

  1. Step 1: Write out the variables that are given in the question, both known and unknown, and use the context of the question to deduce any quantities that aren't explicitly given

  2. Step 2: Choose the equation which contains the quantities you have listed

  3. Step 3: Convert any units to SI units and then insert the quantities into the equation and rearrange algebraically to determine the answer
• This is one of the most important sections of this topic - usually, there will be one, or more, questions in the exam about solving problems with the kinematic equations equations
• The best way to master this section is to practice as many questions as possible!
• Watch out for the direction of vectors: displacement, acceleration and velocity
• Don't worry, you won't have to memorise these, they are give in your data booklet in the exam
• You may sometimes see these equations referred to as 'SUVAT' equations
• Displacement-time graphs


  • Slope equals velocity
  • The y-intercept equals the initial displacement
  • A straight (diagonal) line represents a constant velocity
  • A curved line represents an acceleration
  • A positive slope represents motion in the positive direction
  • A negative slope represents motion in the negative direction
  • A zero slope (horizontal line) represents a state of rest
  • The area under the curve is meaningless
• Velocity-time graphs


  • Slope equals acceleration
  • The y-intercept equals the initial velocity
  • A straight (diagonal) line represents uniform acceleration
  • A curved line represents non-uniform acceleration
  • A positive slope represents acceleration in the positive direction
  • A negative slope represents acceleration in the negative direction
  • A zero slope (horizontal line) represents motion with constant velocity
  • The area under the curve equals the change in displacement
• Acceleration-time graphs


  • Slope is meaningless
  • The y-intercept equals the initial acceleration
  • A zero slope (horizontal line) represents an object undergoing constant acceleration
  • The area under the curve equals the change in velocity
• Acceleration can either be uniform (i.e. a constant value) or non-uniform (i.e. a changing value)
• Motion of a Bouncing Ball

  • The acceleration due to gravity is always in the same direction (in a uniform gravitational field such as the Earth's surface)
  • The ball changes its direction when it reaches its highest and lowest point, so the direction of the velocity will change at these points
  • The vector nature of velocity means the ball will sometimes have a positive velocity if it is travelling in the positive direction, or a negative velocity if it is traveling in the negative direction
  • Ignoring the effect of air resistance, the ball will reach the same height every time before bouncing from the ground again
  • When the ball is traveling upwards, it has a positive velocity which slowly decreases (decelerates) until it reaches its highest point
• Section D of the graph


  • Has the steepest slope
• Largest acceleration


  Is shown in section D
• Calculating the gradient of a velocity-time graph

  Gives the acceleration for that time period
• Drawing a large gradient triangle


  At the appropriate section of the graph
• The acceleration is given by the gradient, which can be calculated using: acceleration = gradient = 5/5 = 1 m s−2
• Therefore, Tora accelerated at 1 m s−2 between 5 and 10 seconds
• Projectile


  A particle moving freely, under gravity, in a two-dimensional plane