Speed/distance help...plz!!!!?

Question

When Gorix escaped from Dr. Sloth's ship, his ship started at rest. Gorix immediately set his thrusters to full power, and his ship's acceleration increased by 2 m/s2 every second for 15 seconds. At that point, the ship remained at constant acceleration for another 30 seconds, after which the thrusters powered off, effectively setting his acceleration to zero.

Disregarding any other forces acting on the ship, how far did Gorix's ship travel after one minute? Please submit your answer in metres, and round to the nearest whole number, if necessary.

Answer 1

Over the first second the average velocity is 1 m/s.  From the end of the first second to the end of second second the average velocity is 3 m/s.  And so forth.  So, over the 45-second acceleration phase the distance covered is

1+3+5+7+9+11+13+15+17+19+21+23

+25+27+29+31+33+35+.......+89 = 2025 m

At the end of the 45-second acceleration phase the velocity is 90 m/s.  Gorix traveled for an additional 15 s at this constant speed and covered an additional 15 x 90 = 1350 m.

Hence, the total distance traveled is 2025 + 1350 = 3375 m.