Motion

• Distance and Displacement

  The magnitude of the length covered by a moving object is called distance. It has no direction.

  Displacement is the shortest distance between two points or the distance between the starting and final positions with respect to time. It has magnitude as well as direction.

  Displacement can be zero, but distance cannot.

  Distance VS Displacement
• Scalar quantities are only expressed as magnitude. E.g.: time, distance, mass, temperature, area, volume
• Vector quantities are expressed in magnitude as well as the direction of the object. E.g.: Velocity, displacement, weight, momentum, force, acceleration
• Time is the duration of an event that is expressed in seconds. It is a scalar quantity
• Speed is the rate of change in distance
• Instantaneous speed is the speed of an object at a particular moment in time
• Average speed is stated as the distance covered by the object within a period of time

  • Average speed = Total distance travelled / Total time taken
• Difference between Average Speed and Instantaneous Speed:

  • Average Speed:
  • Defined as the total distance travelled divided by the total time elapsed
  • Constant
  • Measured by calculating the speed for an entire journey
  • Instantaneous Speed:
  • Defined as the speed at a particular instant of time
  • Not constant
  • Measured by a speedometer
• Uniform motion:

  • Object covers equal distances in equal intervals of time
  • Examples: Movement of the ceiling fan’s blades, Motion of Earth around the sun, Pendulum with equivalent amplitude on either side
• Non-uniform motion:

  • Object covers unequal distances in equal intervals of time
  • Examples: Bouncing ball, Running horse, Moving train
• Velocity is the rate of change of displacement. It is a vector quantity
• Instantaneous velocity is the rate of change of position for a time interval which is very small, i.e. almost zero
• Average velocity is defined as the displacement divided by the time intervals in which the displacement occurs
• Acceleration is the rate of change of velocity, denoted by "a" and is a vector quantity
• In non-uniform motion, velocity varies with time, and the change in velocity is not 0
• Acceleration = Change in Velocity / Time or a = v-u/t, where t is time taken, v is final velocity, and u is initial velocity
• Distance-Time graphs show the change in the position of an object with respect to time
• Linear variation on a Distance-Time graph implies uniform motion, while non-linear variations imply non-uniform motion
• The slope of a Distance-Time graph gives speed
• On a Distance-Time graph:

  • OA implies uniform motion with constant speed
  • AB implies the body is at rest
  • B to C represents non-uniform motion
• Velocity-Time graphs show the change in velocity with respect to time
• The slope of a Velocity-Time graph gives acceleration
• The area under the curve on a Velocity-Time graph gives displacement
• A line parallel to the x-axis on a Velocity-Time graph implies constant velocity
• On a Velocity-Time graph:

  • OA represents constant acceleration
  • AB represents constant velocity
  • BC represents constant retardation
• Equations of Motion for an object moving at uniform acceleration:

  (i) v = u + at

  (ii) v^2 - u^2 = 2as

  (iii) s = ut + (1/2)at^2

  where u is initial velocity, v is final velocity, t is time, a is acceleration, and s is displacement
• Uniform Circular Motion is when an object moves in a circular path with uniform speed
• In Uniform Circular Motion:

  • Velocity changes as direction keeps changing
  • Acceleration is constant
  • The uniform circular velocity is given by u = 2r/t
• Examples of Uniform Circular Motion:

  • Motion of artificial satellites around the Earth
  • Motion of electrons around its nucleus
  • Motion of blades of windmills
  • Tip of the second hand of a watch with a circular dial