Question

A body starts from rest travels a certain distance in time t with constant acceleration. How much
ime will it take to travel last 1/4th distance in terms of t.​

Answer 1

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Answer 2

Given info : A body starts from rest travels a certain distance in time t with constant acceleration.

To find : How much time will it take to travel last 1/4 th distance in term of t.

solution : let body travels x distance in time t with constant acceleration a.

as initial velocity, u = 0

using formula, s = ut + 1/2 at²

⇒x = 0 + 1/2 at²

⇒x = 1/2 at² ........(1)

now velocity after traveling 3x/4 distance :

using formula, v² = u² + 2as

here, u = 0, s = 3x/4

so, v² = 0 + 2a(3x/4) = 3ax/2

v = √(3ax/2)

let time taken to travel last 1/4th distance is t'.

here initial velocity, u = √(3ax/2)

distance covered, s = x/4

using formula, s = ut + 1/2 at²

⇒x/4 = √(3ax/2)t' + 1/2 at'²

⇒(1/2at²)/4 = √(3a × 1/2 at²/2)t' + 1/2 at'² [ from equation (1) ]

⇒1/8 at² = √3 × at/2 × t' + 1/2 at'²

⇒t²/4 = √3 tt' + t'²

⇒4t'² + 4√3tt' - t² = 0

⇒t' = {-4√3 ± √(48 + 16)}t/8

⇒t' = (-4√3 + 8)t/8 = (-√3/2 + 1)t [ time can't be negative so we neglected negative part of roots ]

⇒t' = (1 - √3/2)t

Therefore the time will be taken by the body to travel the last 1/4 th distance in term of t is (1 - √3/2)t