Forces and Motion

• Distance quantity


  Scalar quantity (no specific direction required)
• If an object moves 3 metres to the left and then 3 metres back to its initial position, the object's total displacement is zero
• Displacement is a vector quantity so it also involves direction
• The object starts and ends at the same point, so the displacement is zero
• Typical value for the speed of sound is 330 m/s
• Typical value for human walking speed is 1.5 m/s
• Typical value for human running speed is 3 m/s
• Typical value for human cycling speed is 6 m/s
• Distance = Speed x Time

  Distance (m), Speed (m/s), Time (s)
• An object travelling at a constant speed in a circle cannot have a constant velocity because velocity is a vector quantity and the direction is continuously changing
• Speed from a distance-time graph

  Equal to the gradient of the graph
• To calculate speed at a given time from a distance-time graph for an accelerating object

  1. Draw a tangent to the curve at the required time

  2. Calculate the gradient of the tangent
• Acceleration equation


  • Acceleration = (Change in Velocity)/(Time Taken)
  • Acceleration (m/s²), Velocity (m/s), Time (s)
• Distance from a velocity-time graph

  Equal to the area under the graph
• Approximate value for the acceleration of an object in free fall under gravity near the Earth's surface is 9.8 m/s²
• When an object is falling at terminal velocity, the resultant force acting on it is zero
• Newton's first law for a stationary object


  If the resultant force on a stationary object is zero, the object will remain at rest
• Newton's first law for a moving object

  If the resultant force on a moving object is zero, the object will remain at constant velocity (same speed in same direction)
• When a car is travelling at constant velocity, the braking forces are equal to the driving forces
• If an object changes direction but remains at a constant speed


  There is a resultant force
• Inertia


  The tendency of an object to continue in its state of rest or uniform motion
• Newton's Second Law


  1. Resultant force = Mass x Acceleration

  2. F = ma
• Newton's Second Law


  An object's acceleration is directly proportional to the resultant force acting on it and inversely proportional to its mass
• Inertial mass


  • A measure of how difficult it is to change a given object's velocity
  • The ratio of force over acceleration
• The symbol used to represent an approximate value is ~
• Newton's Third Law


  Whenever two objects interact, the forces that they exert on each other are always equal and opposite
• Stopping distance of a vehicle

  The sum of thinking distance and braking distance
• For a given braking distance, if the vehicle's speed is increased


  The stopping distance is increased
• Human reaction time


  0.2 seconds - 0.9 seconds
• Factors affecting driver's reaction time

  • Tiredness
  • Drugs
  • Alcohol
• Factors affecting braking distance

  • Adverse (wet/icy) road conditions
  • Poor tyre/brake conditions
• Energy transfers when a car applies its brakes

  1. Work is done by the friction force between the brakes and wheel

  2. Kinetic energy of the wheel is converted to heat and is dissipated to the surroundings through the brake discs
• To stop a car in a given distance, if its velocity is increased


  The braking force must also be increased
• Consequences of a vehicle undergoing very large decelerations

  • Kinetic energy converted to heat is very high causing brakes to overheat
  • Loss of control of the vehicle