Answer :

(a) We know,


(1)


(2)


Multiplying the equation (1) with sin and (2) with cos




Adding the above two equations,




Substituting in equation (1),







(b) In order to show that and are perpendicular, lets show that their dot product is zero.




Therefore, and are perpendicular.


(c)


Differentiating on both sides,



(d)


Writing dimensions on both sides,





(e) We know,


Here, a=1



Differentiating on both sides to find velocity,




Differentiating on both sides to find acceleration,




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