A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of `a` metre/`sec^2`, then the resultant acceleration will be

Options

A. `sqrt((v^(2))/(a^(2))+r^(2))`
B. `sqrt((v^(2))/(r)+a)`
C. `sqrt((v^(4))/(r^(2))+a^(2))`
D. `((v^(2))/(r)+a)`

Answer

C

Explanation

`a=sqrt(a_(n)^(2)+a_(t)^(2))=sqrt(((v^(2))/(r))^(2)+a^(2))=sqrt((v^(4))/(r^(2))+a^(2))`