Motion-Notes

•   For a body at rest

•   As the slope is zero, so speed of the body is zero.

      

•   For a body moving with uniform speed

      

•   For accelerated motion.

•   The slope of graph is increasing with time

      

•   For decelerated (speeding down) motion.

•   Slope of graph is decreasing with time

      

•   When a body moving with a uniform velocity.

•   The slope of AB indicates zero acceleration

      

•   When a body starts from rest and moves with uniform acceleration.

•   Greater is the slope of v-t graph, greater will be the acceleration

      

•   When a body is moving with uniform acceleration and its initial velocity is not zero.

      

•   When a body is moving with increasing acceleration.

•   Slope increases with time.

      

•   When a body is moving with decreasing acceleration.

•   Slope decreases with time.

      

•   When a body is moving with a uniform retardation and its initial velocity is not zero.

•   As θ > 90°, graph has a negative slope.

      

•   An object is said to be in motion when its position changes with time.

•   We describe the location of an object by specifying a reference point. Motion is relative. The total path covered by an object is said to be the distance travelled by it.

•   The shortest path/distance measured from the initial to the final position of an object is known as the displacement.

•   Uniform motion: When an object covers equal distances in equal intervals of time, it is said to be in uniform motion.

•   Non-uniform motion: Motions where objects cover unequal distances in equal intervals of time.

•   Speed: The distance travelled by an object in unit time is referred to as speed. Its unit is m/s.

•   Average speed: For non-uniform motion, the average speed of an object is obtained by dividing the total distance travelled by an object by the total time taken.

      

•   Velocity: Velocity is the speed of an object moving in definite direction. S.I. unit is m/s.

      

•   Acceleration: Change in the velocity of an object per unit time.

      

•   Graphical representation of motions

      (i)   Distance-time graph

      For a distance-time graph time is taken on x-axis and distance is taken on y-axis.

      [Note: All independent quantities are taken along the x-axis and dependent quantities are taken along y-axis.]

OA = CD = u

      OE = CB = v

      OC = AD = t

      BD = BC – DC (Change in velocity)

      AD is parallel to OC.

      ∴ BC = BD + DC = BD + OA

      ∴ BC = v and OA = u

      We get v = BD + u

      ∴ BD = v – u             ...(1)

      In velocity-time graph, slope gives acceleration.

      

      Substituting (2) in (1) we get

      BD = v – u

      at = v – u

      ∴ v = u + at

      (ii)   Equation for position-time relation:

      

      Let us assume,

      s = distance travelled by the object

      t = in time t

      a = with uniform acceleration.

      ∴ Distance travelled by the object is given by area enclosed with OABC in the graph.

      ∴ s = OABC

      = (area of rectangle OADC) + (area of DABD)

      

      Substituting

      OA = u, OC = AD = t and BD = at

      We get

      

      (iii)   Equation for position-velocity relation:

      

      s = distance travelled by the object

      t = in time t

      a = moving with uniform acceleration

      s = area enclosed by trapezium OABC

      

      Substitute value of ‘t’ in (1)

      

•   Uniform circular motion: When a body moves in a circular path with uniform speed, its motion is called uniform circular motion.