Graphs and scalar quantities

• Velocity-time graph


  Represents the motion of an object along a straight line
• Velocity-time graph


  • The gradient of the line is equal to the acceleration of the object
  • The area under the graph can be used to calculate the displacement of the object
• Sections of a velocity-time graph

  • Positive gradient, velocity increasing, acceleration positive
  • Zero gradient, velocity constant, acceleration zero
  • Negative gradient, velocity decreasing, acceleration negative
  • Zero velocity, object stationary, acceleration zero
• Calculating displacement from a velocity-time graph

  1. Find the area of the shaded sections under the line

  2. Use geometry (if lines are straight)

  3. Count the squares beneath the line (if lines are curved)
• Distance-time graph


  Graph used to represent the distance travelled by an object over time
• Distance-time graph


  • The gradient of the line is equal to the speed of the object
  • The greater the gradient (and the steeper the line) the faster the object is moving
• Calculating speed from a distance-time graph

  1. Calculate the change in distance

  2. Calculate the change in time

  3. Speed = distance / time
• Distance-time graph


  • Green line from 0 to 4 s
  • Purple line from 0 to 2 s
• The speed of an object can be calculated from the gradient of a distance-time graph
• Accelerating


  When the speed of an object changes, it will be accelerating or decelerating
• Accelerating/decelerating object on a distance-time graph

  • Shown as a curved line
  • Gradient represents speed - increasing, constant, decreasing, or zero
• Calculating speed of an accelerating/decelerating object

  1. Draw a tangent to the curve at the time of interest

  2. Measure the gradient of the tangent
• An object moving at a constant speed but changing direction is also accelerating
• Velocity


  The speed of an object in a particular direction, a vector quantity
• Velocity changes if either the magnitude or the direction changes
• Distance


  Numerical description of how far apart two things are. For example, the distance from Edinburgh to Glasgow is approximately 50 miles.
• Scalar


  A quantity that requires only a size, for example, distance travelled is 20 m.
• Speed


  The distance travelled in a fixed time period, usually one second.
• Rate of change


  The amount of change in the size of a quantity each second.
• Typical speeds


  • Walking: 1.5 m/s
  • Running: 3 m/s
  • Cycling: 6 m/s
  • Car: 13-30 m/s
  • Train: 50 m/s
  • Aeroplane: 250 m/s
• The speed of the wind and the speed of sound also vary
• A typical value for the speed of sound in air is about 330 m/s
• Calculations involving speed, distance and time


  1. Distance travelled = speed × time

  2. s = v × t
• Scalar quantities


  Physical quantities that only have a magnitude or size
• Vector quantities


  Physical quantities that have both a magnitude and a direction
• Scalar and vector quantities are treated differently in calculations
• Calculations involving scalar quantities

  1. Adding scalars

  2. Subtracting scalars
• The sum of scalar quantities can be found by adding their values together
• Scalar quantities can be subtracted by subtracting one value from another
• Scalar quantities


  Physical quantities that have magnitude (size) but no associated direction
• Vector quantities


  Physical quantities that have both magnitude (size) and an associated direction
• Vector quantities


  • Force (20 newtons to the left)
  • Displacement (50 kilometres east)
  • Velocity (11 metres per second upwards)
  • Acceleration (9.8 metres per second squared downwards)
  • Momentum (250 kilogram metres per second south west)
• The direction of a vector can be given in a written description, or drawn as an arrow
• The length of an arrow represents the magnitude of the quantity
• Scalar quantities


  Physical quantities that have magnitude (size) but no direction
• Vector quantities


  Physical quantities that have both magnitude (size) and direction
• Scalar and vector quantities are treated differently in calculations
• Resultant force


  The single force that could replace all the forces acting on an object, found by adding these together
• If all the forces are balanced, the resultant force is zero
• Calculating resultant force of two forces in the same direction

  Add the magnitudes of the two forces together