Question

A particle starts with initial speed U and retardation a to come to rest in time T. The time taken to cover first half of the total path travelled is? ( answer must be in terms of T)

Answer 1

v = u + a t

=> 0 = u - a T substituting values
=> T = u/a

Distance covered before stopping: s = (v² - u²) / (2a)
=> s = (0- u²)/(-2a) = u²/ (2a)

time t to cover half total distance :
s = u t + 1/2 a t²
=> u²/(4a) = u t - 1/2 a t²
=> 2a² t² - 4 au t + u² = 0

=> t = [√2 + 1] u / (√2 a)
The time taken to cover 1st half is > the time taken to cover the second half distance. So we take + sign.

t = T * (√2 + 1)/√2