A particle first accelerates from rest and then retards to rest during the time interval of 8s. If the retardation is 3 times the acceleration, then the time for which it accelerated is

Let t be the time of acceleration

Then retardation time = 8−t 

total time = 8 s

Let V ₁ be velocity after acceleration 

let acceleration be a

V₁​ = u + at
here u = 0

V₁ = at   →(i)

Given retardation = 3a (given)

Hence, V = V₁ − 3a(8−t)

V = 0,

V₁ = 3a(8−t)

at = 3a(8 − t), put V₁

from(i)

t = 24 − 3t

4t = 24

t = 6second