Geo-Scientist Prelims 2024 General Studies Q90: A particle moves in a circle of radius 4 m. Its linear speed is…

A particle moves in a circle of radius 4 m. Its linear speed is given by 4√3 t, where t is the time measured in seconds. At t = 1 s, the angle made by the resultant acceleration – r̂ with direction (+ r̂ is the radial direction) is given by ϕ. Which one among the following is the correct value of ϕ ?

1. (a) \(\tan^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
2. (b) \(\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)\)
3. (c) \(\tan^{-1}\left(\frac{2}{\sqrt{3}}\right)\)
4. (d) \(\tan^{-1}(\sqrt{3})\)