In previous chapter we have learned about the motion of any particle along a straight line
Straight line motion or rectilinear motion is motion in one dimension.Now in this chapter ,we will consider both motion in two dimension and three dimension.
In two dimensional motion path of the particle is constrained to lie in a fixed plane.Example of such motion motion are projectile shot from a gun ,motion of moon around the earth,circular motion and many more.
To solve problems of motion in a plane,we need to generalize kinematic language of previous chapter to a more general using vector notations in two and three dimensions.
Consider a particle moving along a curved path in x-y plane shown below in the figue
Suppose at any time,particle is at the point P and after some time 't' is at point Q where points P and Q represents the position of particle at two different points.
Position of particle at point P is described by the Position vector r from origin O to P given by r=xi+yj
where x and y are components of r along x and y axis
As particle moves from P to Q,its displacement would be would be Δr which is equal to the difference in position vectors r and r'.Thus
Δr = r'-r = (x'i+y'j)-(xi+yj) = (x'-x)i+(y'-y)j = Δxi+Δyj (1)
where Δx=(x'-x) and Δy=(y'-y)
If Δt is the time interval during which the particle moves from point P to Q along the curved path then average velocity(vavg) of particle is the ratio of displacement and corresponding time interval
since vavg=Δr/Δt , the direction of average velocity is same as that of Δr
Magnitude of Δr is always the straight line distance from P to Q regardless of any shape of actual path taken by the particle.
Hence average velocity of particle from point P to Q in time interval Δt would be same for any path taken by the particle.