 # Distance and Displacement

Distance: The length of the actual path travelled by a particle between the initial and final position of it in a given interval of time is called distance. Distance is the scalar quantity.

SI unit of distance is meter (m) and dimension is [L].

Displacement: The shortest distance travelled by a particle between the initial and final position of it in a given interval of time is called displacement. Displacement is the vector quantity.

SI unit of displacement is meter (m) and dimension is [L].

A particle moves in a circular path of radius r and comes to its initial position. The distance travelled by it is and displacement is zero.

A particle moves in a straight path towards east for x unit and then towards north for y unit. The distance travelled by it is (x + y) and the displacement is . CONCEPT: A wheel of radius r rotates on a horizontal surface. Find the displacement of the point which touches the ground during half rotation.

Let us consider a point P of wheel touches the surface and after half rotation of the wheel that point (P) moves to and the point which touches the surface at that instant is .

So, the horizontal displacement of the point P is and vertical displacement of the point P is . So, net displacement of the point P is  . CONCEPT: If initial velocity (u) is antiparallel to the acceleration (a) of the body, then the motion is retarded first and then accelerated.

Example: A ball is thrown vertically upwards with initial speed u. The time taken by the ball to travel maximum height is = .

If the given time t < , then distance(s) = displacement(s) = ut – g .

If the given time t = , then distance(s) = displacement(s) = ut – g .

If the given time t > , then displacement(s) = ut – g and

Distance (s) = + g . [Distance travelled by upward motion is = and distance travelled by downward motion in remaining time is = g .]

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