The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R =2 ~m . Another car approaches him from behind with a uniform speed of 90 ~km / hr . When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a i

Step-by-step solution

aligned & v = uf u - f = -24 1 -24-1 = 24 25 & ~m = - v u =- 24 25(-24) = 1 25 & 1 v - 1 u = 1 f & v _ I =- m ^2 v ₀= -1 (25)^2 25= -1 25 aligned Diff. aligned & -1 v ^2 ( dv dt )+ 1 u ^2 ( du dt )=0 [ dv dt = v _ i ; du dt = v ₀ ] & +2 v ^3 ( v _ t )^2- 1 v ^2 a _ L - 2 u ^3 ( v ₀ )^2+ 1 u ^2 a ₀=0 & a _ I v ^2 = 2 v ^3 v _ I ^2- 2 u ^3 v ₀^2 & a _ I = 2 v v _ I ^2- 2 v ^2 u ^3 v ₀^2 & = 2 25 24 1 25 1 25 - 2 (24)^3 24 25 24 25 25 25 & a _ I = 2 24.25 - 2 24 & a ₁= 2 24 -24 25 = -2 25 & 100 a₁= 2 25 100=8 aligned