Change in velocity is vector subtraction . Take the final velocity vector , at the end of the arrow join the negative vector of the initial velocity, then join the start to the end and then that is the change in velocity vector (same as add vector). If use component method the do two times . First change in velocity (x-comp) is vf-vi. Then change in velocity (y-comp) is also vf-vi. Then use pythagoras theorem to find resultant change in velocity vector and tangent to find angle of the final vector.Seldom used because its very long .For circular motion, draw a small sector , draw tangential velocity , one will be initial and the other final velocity. Bring the initial to the final (but change the arrow) as is -ve vector .Join the start to the end and the change in velocity point towards the centre of the circle (nearly) . As the sector is smaller and smaller , then it will point to the centre.
