Notes On Motion with Constant Acceleration and Relative Velocity in Two Dimensions - CBSE Class 11 Physics
Consider a body moving in the x-y plane with a constant acceleration a. It is located at point P at time t = 0, which has a position coordinate r0 and velocity v0. It reaches point P’ at time t, has a position coordinate r and velocity v. Constant acceleration a is equal to change in velocity by time. Average velocity = displacement/time.
 

 
 These equations imply that a body can have two independent simultaneous motions in x and y directions with constant acceleration. Similar equations can be written for three-dimensional motion also.
 
Relative velocity: Consider two bodies A and B moving in the x-y plane with velocities VA and VB, respectively, with respect to the co-ordinate system. The velocity of A with respect to B is written as VAB .
 
When subtracting two vectors, to obtain the relative velocity vector, reverse the second vector and add the two vectors. 

Summary

Consider a body moving in the x-y plane with a constant acceleration a. It is located at point P at time t = 0, which has a position coordinate r0 and velocity v0. It reaches point P’ at time t, has a position coordinate r and velocity v. Constant acceleration a is equal to change in velocity by time. Average velocity = displacement/time.
 

 
 These equations imply that a body can have two independent simultaneous motions in x and y directions with constant acceleration. Similar equations can be written for three-dimensional motion also.
 
Relative velocity: Consider two bodies A and B moving in the x-y plane with velocities VA and VB, respectively, with respect to the co-ordinate system. The velocity of A with respect to B is written as VAB .
 
When subtracting two vectors, to obtain the relative velocity vector, reverse the second vector and add the two vectors. 
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