A car initially travelling eastwards turns noth by travelling in a quarter circular path of radius `R` metres at uniform speed as shown in figure. The car completes the turn in `T` second.
`(a)` What is the acceleration of the car when it is at `B` located at an angle of `37^(@)`. Express your a swers in terms of unit vectors `hat(i)` and `hat(j)`.
`(b)` The magnitude of car's average acceleration during `T` second period.

Answer

A, B, C, D

Explanation

Speed of car `v=(pi R)/(2T) m//s`
`(a)` The acceleration of car is `(v^(2))/(R)=(pi^(2)R)/(4T^(2))` at `B` and is directedd from `B` to `O`.
`:. ` Acceleration vector of car at `B` is
`vec(a)=(v^(2))/(R)(-sin 37^(@) hat (i)+cos 37^(@)hat(j))=(pi^(2)R)/(20T^(2)) (-3hat(i)+4hat(j)) m//s^(2)`
`(b)` The magnitude of average acceleration of car is time `T` is
`(|vec(V)_(C)vec(V)_(B)|)/(T)=(sqrt(v))/(T)=(piR)/(sqrt(2)T^(2))m//s^(2)`