Motion

• Rest: A body is in a state of rest when its position doesn't change with respect to a reference point
• Motion: A body is in a state of motion when its position changes continuously with reference to a point
• Motion can be of different types: Circulatory motion, Linear motion, Oscillatory motion
• Scalar quantity: Physical quantity with magnitude but no direction. Example: distance, speed
• Vector quantity: Physical quantity with magnitude and direction. Example: displacement, velocity
• Distance: Actual path or length traveled by an object from initial to final position
• Displacement: Requires both magnitude and direction. Can be zero when initial and final points are the same
• Uniform Motion: Body travels equal distance in equal time intervals
• Non-uniform Motion: Body travels unequal distances in equal time intervals
• Two types of non-uniform motion: Accelerated Motion and De-accelerated Motion
• Speed: Measurement of distance traveled by a body per unit time
• Average speed: Total distance traveled divided by total time taken
• Conversion Factor: Change from km/hr to m/s = 5/18 m/s
• Velocity: Speed of a body in a given direction
• SI unit of velocity: m/s
• Average velocity: Total displacement divided by total time
• Acceleration: Seen in non-uniform motion
• Distance travelled during the 3rd hour = 30 km
• Average speed = Total distance travelled / Total time taken = (20 + 40 + 30) / 3 = 90 / 3 = 30 km/hr
• Acceleration is seen in non-uniform motion and can be defined as the rate of change of velocity with time
• Acceleration (a) = Change in velocity / Time = (v - u) / t, where v = final velocity, u = initial velocity
• If v > u, then acceleration 'a' will be positive (+ve)
• Retardation/Deceleration is seen in non-uniform motion during a decrease in velocity with time
• Deceleration (a') = Change in velocity / Time = (v - u) / t, where v < u, 'a' = negative (-ve)
• Example 1: A car's speed increases from 40 km/hr to 60 km/hr in 5 sec. Calculate the acceleration of the car
• Example 2: A car travelling at a speed of 20 km/hr comes to rest in 0.5 hrs. Calculate the value of its retardation
• Graphical Representation of Equations:
• Distance-Time Graph (s/t graph):

  • s/t graph for uniform motion
  • s/t graph for non-uniform motion
  • s/t graph for a body at rest
• Velocity-Time Graph (v/t graph):

  • v/t graph for uniform motion
  • v/t graph for uniformly accelerated motion
  • v/t graph for non-uniformly accelerated motion
  • v/t graph for uniformly decelerated motion
  • v/t graph for non-uniformly decelerated motion
• Equation of Motion (For Uniformly Accelerated Motion):

  • First Equation: v = u + at
  • Second Equation: s = ut + 1/2 at^2
  • Third Equation: v^2 = u^2 + 2as
• Example 1: A car starting from rest moves with uniform acceleration of 0.1 m/s^2 for 4 mins. Find the speed and distance travelled
• Example 2: Brakes applied to a car produce deceleration of 6 m/s^2 in the opposite direction to the motion. If the car requires 2 sec to stop, calculate the distance travelled by the car during this time
• Uniform Circular Motion:

  • If a body moves in a circular path with uniform speed, it is executing uniform circular motion
  • In such motion, the speed may be the same throughout, but its velocity is different at each point, making it an accelerated motion