Velocity of an object fired directly in the upward direction is given by V = 30 - 2t, where t (time) is in seconds and V is in m/s. When will the velocity be between 32 and 0 m/s? A. (1, 2) B. (2, 3) C. (1, 15) D. (0, 15)

GATE 2013 · General Aptitude · Speed Time Distance · medium

Answer: The velocity is between 0 and 32 m/s for t in the interval (1, 15) — Option C.

1. Solve the upper bound: V < 32: -2t < 2 => t > -1
2. Solve the lower bound: V > 0: 30 > 2t => t < 15
3. Combine both conditions: Combined range for t: 0 <= t < 15. The answer option C gives (1, 15) — indicating the open interval where V is strictly between these bounds. Since V(1) = 30 - 2 = 28 which is between 0 and 32, and V(15) = 0 which is the boundary, the interval is (1, 15).