In two-dimension motion a body moves in a plane. e.g. a particle rolling in a circle, a cricket ball caught by a fielder. In the first case the body can go round with a constant velocity or it could move with a non-constant velocity. In the second part the cricket ball in a projectile i.e. it has been thrown and it goes under the operation of gravity. This motion is projectile motion.
(i) Position and Displacements: As we had done in one-dimensional linear motion, the first task for us is to check where the body is i.e. its position. The location here is a vector intends from a reference point to the body.
In the unit vector presentation it may be defined, 
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Where  are the vector element  of and the coefficients x and y are its scalar element.
The coefficients of x and y provide the objects location along the axes and relative to the origin. Figure defines particle P whose position vector at an instant is 
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As the body moves its position vector (P.V.) modifies such that the vector always extends to the body from origin.
Considering the particle has a 
at time t1 and 
at time t2, its displacement is 
In the mean time interval 
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(i) Velocity and Average velocity: If a particle goes through a displacement in a time interval Δt, then the average speed is
Here are 
and 
are x and y elements of average velocity.
The instantaneous velocity, 
But 
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then elements of  along x-axis and y-axis respectively.
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In following diagram particle is at  at t1 and at  at t2 (= t1+ t2). The vector is the particle displacement in time . Then as it is clear from (1) average velocity points in similar direction as
Now if we remove Δt we see that
(1) vector goes towards
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(2) goes smaller and its direction tends to the tangent
3) In the limit Δt→0, , the instantaneous speed at t1 i.e. average velocity becomes instantaneous velocity , which has the direction along tangent line.
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