A point moves along an arc of a circle of radius R. Its velocity depends on the distance covered s as `v=asqrts`, where a is a constant. Find the angle `alpha` between the vector of the total acceleration and the vector of velocity as a function of s.

Options

A. `tan^(-1)((s)/(R ))`
B. `tan^(-1)((2s)/(R ))`
C. `tan^(-1)((s)/(2R))`
D. `tan^(-1)((R )/(s))`

Answer

B

Explanation

`v=asqrt(s)`
`a_(c)=(v^(2))/(R )=(a^(2)s)/(R )`
`v=as^((1)/(2))`
`(dv)/(ds)=axx(1)/(2)s^(-(1)/(2))=(a)/(2sqrt(s))`
`a_(t)=v(dv)/(ds)=asqrt(s)xx(a)/(2sqrt(s))=(a^(2))/(2)`
`tan theta=(a_(c))/(a_(t))=(a^(2)s//R)/(a^(2)//2)=(2s)/(R )`
`theta=tan^(-1)((2s)/(R ))`