Motion

MOTIONMotionIf the position of an object changes as the time passes with respect to a reference point, then it is said to be in motion.Scalar QuantitiesThe physical quantities which only have magnitude and no direction are called scalar quantities.Ex – Mass, distance, speed, time, work, energy, power etcVector QuantitiesThe physical quantities which have both magnitude and direction (and which can be operated mathematically only by vector algebra) are called vector quantities.Ex - Displacement, velocity, acceleration, momentum, force etcDistanceDisplacementLength of the path covered by a bodyIt is the straight line distance between the initial and the final position of a body.It is a scalar quantity.It is a vector quantity.For a moving body it is always positive.For a moving object it can be positive, negative or zero.It is never decreased during a motion.It can increase or decrease during a motion.It is always more than or equal to the displacement covered.It is always less than or equal to the distance covered.SpeedSpeed of a body indicates how fast it is moving and is given by the distance covered by the body per unit time. Its SI unit is m/s. It is a scalar quantity.Average speedIt is defined as the total distance covered by a body in a given time interval.(a) If a body covers a distance S1 in times T1, S2 in the time T2 and so on, then (b) If a body covers a distance S1 with a speed V1, distance S2 with a speed V2 and so on, then(c) If a body covers first distance with a speed V1 in time T1, the next with a speed V2 in time T2 and so on, then(d) If a body covers a distance with a speed u and an equal distance with a speed v, thenUniform SpeedIf a body covers equal distance in equal time intervals however small the time interval be, the body is said to move the uniform Speed.Velocity The velocity of a body indicates how fast it is moving in a given direction and it is given by the displacement covered by the body per unit time. Its SI unit is m/s. It is a vector quantity.Average Velocity It is defined as the total displacement of the body in a given time interval divided by the time interval.If the velocity of a body changes from u to v uniformly (uniform acceleration), thenUniform VelocityIf a body covers equal distances in equal time intervals moving in a particular direction, it is said to move with uniform velocity. This motion is called uniform motion.AccelerationThe rate of change of velocity of a body is called its acceleration. Its SI unit is m/s2. It is a vector quantity.or Equations of motion by graphical methodConsider a body uniformly increasing its velocity from u to v in time interval t. In the graphInitial velocity is represented by OA = EC = uFinal velocity is represented by OD = BC= vTime is represented by OC = AE = AB = tAcceleration of the body is given by or or or or or or This is the first equation of motion..Displacement covered by the body is given byor .or or or or or or or [(or This is the second equation of motion.Displacement covered by the body is given byor .or or or or or [(or or or This is the third equation of motion.Uniform circular motionIf a body moves on a circular path with a constant speed, its motion is said to be uniform circular motion.Consider a body executing uniform circular motion in a circle of radius r with a constant speed v, then time taken to complete on revolution is given byr or or