# Motion in a plane

**1. Introduction**

- 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.

## 2.Average velocity

- 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**=x**i**+y**j**

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 Δ
**r** which is equal to the difference in position vectors **r** and **r'**.Thus

Δ**r** = **r'**-**r** = (x'**i**+y'**j**)-(x**i**+y**j**) = (x'-x)**i**+(y'-y)**j** = Δx**i**+Δy**j** (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(
**v**_{avg}) of particle is the ratio of displacement and corresponding time interval

since **v**_{avg}=Δ**r**/Δt , the direction of average velocity is same as that of Δ**r**

- Magnitude of Δ
**r** 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.

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