Question

why did you changed the sign of acceleration for finding retardation

Answer 1

because the retardation means, force applied in the opposite direction of the momentum, so the force applied to do retardation is opp of the momentum of the object.
that is why we take it as negative

Answer 2

Retardation is negative acceleration.
When we increase velocity with time, we get acceleration but when we decrease velocity with time, we get retardation so, retardation is actually a negative acceleration. Therefore, we need to change positive sign to negative for finding retardation.

Thanks.