Distance, displacement, speed and velocity

• Distance


  Just how far an object has moved. It's a scalar quantity so it doesn't involve direction.
• Displacement


  A vector quantity that measures the distance and direction in a straight line from an object's starting point to its finishing point.
• Speed


  How fast you're going, a scalar quantity with no regard to direction.
• Velocity


  Speed in a given direction, a vector quantity.
• You can have objects travelling at a constant speed with a changing velocity when the object is changing direction whilst staying at the same speed.
• Calculating distance, speed and time

  distance travelled (m) = (average) speed (m/s) x time (s)
• Vectors


  • Have magnitude (size) and direction
• Vector quantities


  • force
  • velocity
  • displacement
  • weight
  • acceleration
  • momentum
• Scalar quantities


  • speed
  • distance
  • mass
  • energy
  • temperature
  • time
• Typical speeds for different transport methods

  • Walking - 14 m/s (5 km/h)
  • Running - 3 m/s (11 km/h)
  • Cycling - 5.5 m/s (20 km/h)
  • Cars in a built-up area - 13 m/s (47 km/h)
  • Aeroplanes - 250 m/s (900 km/h)
  • Cars on a motorway - 31 m/s (112 km/h)
  • Trains - up to 55 m/s (200 km/h)
  • Wind speed - 5-20 m/s
  • Speed of sound in air - 340 m/s
  • Lorries - 15 m/s (54 km/h)
• Objects rarely travel at a constant speed. E.g. when you walk, run or travel in a car, your speed is always changing.
• Acceleration


  Speeding up (or slowing down) at a constant rate
• Acceleration is not the same as velocity or speed
• Acceleration


  The change in velocity in a certain amount of time
• Finding average acceleration


  1. a = (v-u)/t

  2. Where u is initial velocity, v is final velocity, t is time
• Deceleration


  Negative acceleration (when something slows down)
• You need to be able to estimate accelerations
• Uniform acceleration


  Constant acceleration
• Acceleration due to gravity

  • Uniform, roughly 10 m/s² near Earth's surface, same as gravitational field strength
• Equation for uniform acceleration

  1. v² = u² + 2ax

  2. Where v is final velocity, u is initial velocity, a is acceleration, x is distance
• Distance-time graph


  Gradient (slope) gives speed, flat sections are constant speed, steps are changing speed, curves are changing acceleration
• Finding speed from distance-time graph

  1. For straight line, speed = gradient

  2. For curved line, draw tangent and find gradient of tangent
• Velocity-time graph


  Gradient is acceleration, flat sections are constant speed, uphill is acceleration, downhill is deceleration, curves are changing acceleration
• Area under velocity-time graph


  Equals distance travelled
• Newton's First Law


  An object at rest stays at rest, and an object in motion stays in motion, unless acted on by an unbalanced force
• Newton's Second Law


  Acceleration is proportional to the resultant force and inversely proportional to the mass
• Calculating resultant force


  1. F = m x a

  2. Where F is resultant force, m is mass, a is acceleration
• Mass


  Amount of 'stuff' in an object, measured in kilograms
• Weight


  Force acting on an object due to gravity, measured in newtons
• Calculating weight


  1. W = m x g

  2. Where W is weight, m is mass, g is gravitational field strength
• Centripetal force


  Force that keeps an object moving in a circle
• Velocity is constantly changing in circular motion, so there must be a resultant force
• Large decelerations can be dangerous due to the large forces involved
• Safety features like seatbelts and crumple zones reduce the force in a collision
• Brakes can overheat and cause skidding with very large decelerations
• Inertia means the trolley's mass and the accelerating force affect its acceleration
• The main cause of the trolley accelerating as it travels down the ramp will be the force due to gravity caused by the hanging mass
• Acceleration


  Depends on the mass of the trolley and the size of the accelerating force
• Investigating the effect of the trolley's mass

  1. Add masses one at a time to the trolley

  2. Keep the mass on the hook constant (so the accelerating force is constant)

  3. Repeat steps 2-5 of the experiment each time
• Investigating the effect of the accelerating force

  1. Start with all the masses loaded onto the trolley

  2. Transfer the masses to the hook one at a time

  3. Repeat steps 2-5 each time you move a mass