Describing motion

• Distance is a numerical description of how far apart two things are
• Distance does not include an associated direction, making it a scalar quantity
• Speed is the rate of change of distance, measured as the distance travelled per unit time
• Speed is also a scalar quantity, as it does not have an associated direction
• Some typical speeds in metres per second (m/s) include:

  • 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 sound in air is approximately 330 m/s
• The equation to calculate distance travelled by an object moving at constant speed is: distance = speed × time (s = v * t)
• In the equation, distance is measured in meters (m), speed in meters per second (m/s), and time in seconds (s)
• To calculate average speed, divide the total distance travelled by the total time taken
• Velocity is the speed of an object in a particular direction
• Velocity is a vector quantity because it has both magnitude and direction
• To calculate velocity, displacement is used in calculations, rather than distance
• Displacement is a vector quantity that includes the distance traveled and the direction of the straight line from start to finish
• Acceleration is the rate of change of velocity, measured in meters per second squared (m/s²)
• The change in velocity can be calculated using the equation: change in velocity = final velocity - initial velocity
• The average acceleration of an object can be calculated using the equation: acceleration = change in velocity / time taken
• If an object is slowing down, it is decelerating and its acceleration has a negative value
• Acceleration (α) is measured in meters per second squared (m/s²), change in velocity (∆v) is measured in meters per second (m/s), and time taken (t) is measured in seconds (s)
• In a 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
• The speed of an object can be calculated from the gradient of a distance-time graph
• If the speed of an object changes, it will be accelerating or decelerating
• Acceleration is the rate of change in speed and is measured in metres per second squared
• On a distance-time graph, accelerating or decelerating objects are represented by curved lines
• Different sections of a distance-time graph represent different speeds:

  • Section A: Increasing gradient, increasing speed
  • Section B: Constant gradient, constant speed
  • Section C: Decreasing gradient, decreasing speed
  • Section D: Zero gradient, stationary (at rest)
• To calculate the speed of an accelerating or decelerating object at a particular time:

  • Draw a tangent to the curve at that time
  • Measure the gradient of the tangent
  • Calculate speed using the formula: speed = vertical change (A) / horizontal change (B)
• An object moving at a constant speed but changing direction continually is also accelerating
• Velocity is the speed of an object in a particular direction and is a vector quantity
• Velocity changes if either the magnitude or the direction changes, which is important in dealing with circular motion
• Motion in a straight line can be represented by a velocity-time graph
• The gradient of the line on a velocity-time graph represents the acceleration of the object
• Different sections of a velocity-time graph represent:

  • Positive gradient: Increasing velocity and positive acceleration
  • Zero gradient: Constant velocity and zero acceleration
  • Negative gradient: Decreasing velocity and negative acceleration
  • Gradient of zero (v=0): Stationary (at rest) velocity and zero acceleration
• Displacement of an object can be calculated from the area under a velocity-time graph
• Displacement is the quantity describing the distance from the start of the journey to the end in a straight line with a described direction
• To calculate displacement:

  • Find the area of the shaded sections under the graph
  • Use geometry for straight lines or count squares for curved lines
• The equation for objects in uniform acceleration is: \(v^2 - u^2 = 2~a~s\)
• Final velocity (v) is measured in metres per second (m/s)
• Initial velocity (u) is measured in metres per second (m/s)
• Acceleration (a) is measured in metres per second squared (m/s^2)
• Displacement (s) is measured in metres (m)