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 1

Answer:

There is redundancy in the data given.

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

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We can also find the velocity v at  distance s/2 and then find t.

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