kinematics

• Magnitude of displacement

  May be zero if the displacement is zero
• Average velocity

  Equal to the total displacement divided by the time interval
• Average speed

  Equal to the total path length divided by the time interval
• Magnitude of displacement

  Equal to the average velocity in the corresponding time interval
• Magnitude of displacement

  Equal to the average speed in the corresponding time interval
• Uniform motion


  Velocity is the same at all instants
• Instantaneous speed

  Equal to the magnitude of the instantaneous velocity at that instant
• Instantaneous velocity

  Equal to the average velocity over an infinitesimally small time interval
• Constant acceleration

  Average acceleration equals the constant value during the interval
• Acceleration and velocity cannot change value abruptly at an instant, changes are always continuous
• Object near the surface of the Earth

  Accelerated downward due to gravity
• Free fall

  When air resistance is neglected
• Acceleration due to gravity (g)

  Taken as a constant
• Stopping distance

  Proportional to the square of the initial velocity
• The area under the velocity-time graph is equal to the displacement of the particle during that interval
• The sign of acceleration does not necessarily imply the direction of the particle's displacement
• A particle's speed at an instant does not imply it has zero velocity at that instant
• A particle thrown up has zero velocity at its highest point
• Assertion : the boat must move an angle inclined more than 90° to the direction of flow of river

  reason : a component of velocity of boat must oppose the flow of river

  • both assertion and reason are true and reason is correct explanation of assertion
• assertion : a cyclist must bend while taking a turn

  reason : bending generates required centripetal force for circulatory motion to take place

  • both assertion and reason are true and reason is correct explanation of assertion
• the area under the velocity time graph gives the displacement of the body
• the negative slope of velocity time graph indicates a retarded motion
• At limit, average acceleration becomes the instantaneous acceleration


  1. y = ax² + bx + c

  2. Equation of parabola
• Centripetal acceleration

  • Not a constant vector
• Motion in a plane

  Can be treated as superposition of two separate simultaneous one-dimensional motions along two perpendicular directions
• horizontal range , R is maximum at angle 45°
• until vector is dimensionless and unitless