Motion, Speed, Velocity and Acceleration

MOTION, SPEED, VELOCITY AND ACCELERATION


1. Motion


Definition:
When a body changes its position with respect to time, it is said to be in motion.


Example: A moving car, flowing river, or running boy.


2. Rest


Definition:
When a body does not change its position with time, it is said to be at rest.


Example: A book lying on a table.


3. Types of Motion



  1. Linear (or Translatory) Motion


    • The motion of an object along a straight line.

    • Example: A car moving on a straight road.


  2. Circular Motion


    • The motion of an object along a circular path.

    • Example: The rotation of a fan blade or a planet moving around the Sun.


  3. Periodic Motion


    • The motion that repeats itself after equal intervals of time.

    • Example: The swinging of a pendulum or the beating of a human heart.


  4. Rotational Motion


    • When a body spins about its own axis.

    • Example: A spinning top or the Earth rotating on its axis.



4. Distance and Displacement


(a) Distance:



  1. The total path length covered by a moving object.

  2. It tells us how much ground an object has covered.

  3. It is a scalar quantity (it has only magnitude, no direction).

  4. Unit: metre (m)

  5. Example: If a boy walks 3 m east and then 4 m west, the total distance = 3 + 4 = 7 m.


(b) Displacement:



  1. The shortest straight-line distance between the initial and final positions of an object.

  2. It shows how far and in which direction an object is from its starting point.

  3. It is a vector quantity (has both magnitude and direction).

  4. Unit: metre (m)


5. Speed



  • Definition:
    The rate of change of distance with time.


Formula: Speed = Distance / Time


Unit: metre/second (m/s)


Types of Speed



  1. Uniform Speed – Equal distances covered in equal time intervals.
    Example: A train moving at a constant 60 km/h.

  2. Non-uniform Speed – Unequal distances in equal time intervals.
    Example: A bus in traffic.

  3. Average Speed –


Average Speed = Total Distance / Total Time



  1. Instantaneous Speed – Speed at a particular moment.
    Example: Speed shown by a car’s speedometer.


6. Velocity


Definition:
The rate of change of displacement with time.


Formula: Velocity = Total Displacement / Total Time


Unit: metre/second (m/s)


Types of Velocity



  1. Uniform Velocity – Equal displacements in equal time intervals in a fixed direction.

  2. Non-uniform Velocity – Unequal displacements in equal time intervals.

  3. Average Velocity – Average Velocity = Total Displacement / Total Time


Note:
Speed is scalar, but velocity is vector (has both magnitude and direction). 


7. Acceleration


Definition:
The rate of change of velocity with time.


Formula:


Acceleration = Change in Velocity / Time ​


Unit: metre/second² (m/s²)


8. Equations of Uniformly Accelerated motion


For motion starting with initial velocity u, final velocity v, time ttt, displacement s, and acceleration a:



  1. V = u+at

  2. S = ut+1/2at2

  3. v2 = u2+2as


9. Special Notes



  • Speed is scalar, while velocity and acceleration are vector quantities.

  • At the highest point of projectile motion,


    • Velocity = 0, but acceleration ≠ 0 (gravity acts downward).


  • If displacement = 0, velocity = 0,
    but speed may not be zero (example: a runner completing one full circle).


Example: A runner runs around a circular track and returns to the starting point — distance is covered, but displacement = 0.