Udit Gupta is teaching live on Unacademy Plus
Motion in 1D - 1 Compiled by: Udit Gupta Alumnus MNNIT Allahabad Ex-Manager at Reliance Industries Limited Ex-VidyaMandir Faculty of Physics Cofounder and HOD Physics Elements Azamgarh
Content Introduction Position Displacement . Distance Problems on displacement and distance
Introduction . This is the topic where we start mechanics In vectors we learnt how to deal with those quantities and now we will see their application. Mechanics is broadly divided in two topics namely kinematics and dynamics. In kinematics we deal with the motion of the particle (position, displacement, velocity and acceleration) not concerned with the factors producing that motion.
Position It refers to the location of a particle in space at a certain moment of time. Generally, this position is measured by a vector called position vector r) which is a line joining origin (fixed point) to the position of the particle.
Displacement . It is a vector joining initial position to the final position of a particle during a certain interval of time. We can simply say that the change in position of a moving particle is its displacement (s)
Distance It is the length of the actual path traversed by a particle. We can simply call it the length of path travelled by the particle. It is generally denoted by s or x.
Problem 1 An old person moves on a semi-circular track of radius 40.0m during a morning walk. If he starts at one end of the track and reaches at the other end, find the distance covered and the displacement of the person.
Problem 1 . Distance = length of track = x 40.0m = 126m . Displacement-diameter of the semi-circular track = 2r = 80m 40m
Problem- 2 A table clock has its seconds hand 4.0 cm long. Find the displacement and the distance of the tip of the seconds hand: (a) 30 seconds apart (b) 150 seconds apart.
Problem- 2 (a) In 30 seconds, the tip of seconds hand moves diametrically to the opposite side. Displacement = 8.0 cm Distance = (4) = 4 cm (b) In 150 seconds, the displacement is still the same but distance increases. Distance = 2(2 (4)) + (4) = 20