Velocity Question?

Question

A space ship, starting at rest, immediately sets its thrusters to full power, and the 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 its acceleration to zero.

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

Answer 1

a = 2t, t ≤ 15 s

v = t^2,  t ≤ 15 s

s(15) = (1/3)(15^3) =  1,125 m

v(15) = 225 m/s

a(15) = 30 m/s^2

v(45) = 225 m/s + (30 m/s^2)(30 s) = 1,125 m/s

s(45) = 1,125 m + (225 m/s)(30 s) + (1/2)(30 m/s^2)(30 s)^2

s(45) = 21,375 m

s(60) = 21,375 m + (1,125 m/s)(15) = 38,250 m