Mars or Bust

The acceleration due to gravity at the face of the earth is 9.8 meters per second². If you were to get in a space craft and accelerate at a continuous 9.8 meters per second² toward Mars, travel half way, and then turn your spacecraft around and decelerate at the same rate so that you will slow down and be able to land when you reach your destination, how long would it take to reach Mars? Of course, you will be smart and plan your trip when the planets align so as to make the shortest possible flight.

Answer:
1.46 days.

Calculation:
The distance from the earth to the sun is 149,598,261 km. The distance from the sun to Mars is 227,939,100. The shortest distance between the two planets, then, is 227,939,100 - 149,598,261 = 78,340,839 km. = 78,340,839,000 meters.
The midway point, then, would be at 78,340,839,000 / 2 = 39,170,419,000 meters.
Distance = velocity x time.
Since we will be accelerating (and decelerating) at a constant rate, our average velocity will be our final velocity divided by two: v_a = v_f/2.
Our final velocity will be our acceleration times the length of time to reach the halfway point.
Therefore:
Distance = velocity x time.
Distance = v_f/2 x time = ( (time x acceleration)/ 2 ) x time = ( (time x 9.8 m/s/s ) / 2) x time.
2 x Distance = time x 9.8 m/s/s x 2 x time = time² x 2 x 9.8 m/s/s.
(2 x Distance) / 2 x 9.8 m/s/s = time².
Distance / 9.8 m/s/s = time².
39,170,419,000 meters / 9.8 m/s/s = time² (in seconds).
3996981582 seconds = time².
time (to reach the midway point) = square root of 3996981582 = 63221 seconds.
There are 24 x 60 x 60 = 86400 seconds in a day.
Therefore the total time in days is: (2 x 63221 seconds) / 86400 seconds/day = 1.46 days.