Moderate# Constant Acceleration: Time of Flight

CLMECH-L4BUUY

When traveling between planets, it has been suggested that artificial gravity could be provided by constantly accelerating the rocket until the half-way point is reached and then the ship would decelerate for the remainder of the trip. Suppose a ship is to make a $1.00\times 10^9\,km$ trip.

If it accelerates at $9.81\,\frac{m}{s^2}$ from rest to the halfway point and then decelerates for the remainder of the trip, how long would the entire trip take?