A point moves in the x y -plane according to the following equation, x=a t , y=a(1- t) , where a and are positive constants. Find the angle between the point's velocity and acceleration vectors.

Step-by-step solution

Displacement vector, aligned s & =x( i )+y( j ) & =a ( t)( i )+a[1- ( t)]( j ) aligned Velocity vector, aligned v & = d s d t = d d t [a ( t)( i )+a 1- ( t) ( j )] & =a ( t)( i )+a[0- - ( t) ]( j ) & =a ( t)( i )+a ( t)( j ) aligned Acceleration vector, aligned a = d v d t & = d d t [a ( t)( i )+a ( t)( j )] & =-a ^2 ( t)( i )+a ^2 ( t)( j ) aligned Now, calculation of angle between v and a = v a | v || a | [a ( t)( i )+a ( t)( j )] array r = [-a ^2 ( t)( i )+a ^2 ( t)( j ) ] [a ( t)]^2+[a ( t)]^2 [-a ^2 ( t) ]^2+