Velocity of an object fired directly in upward direction is given by V=80−32t, where t (time) is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?
Options:
(A) (1, 3/2)
(B) (1/2, 1)
(C) (1/2, 3/2)
(D) (1, 3)
Official Answer Key:
C
Step-by-Step Solution & Explanation
Solve 32 < 80−32t < 64 as two inequalities:
80−32t > 32 ⇒ −32t > −48 ⇒ t < 1.5
80−32t < 64 ⇒ −32t < −16 ⇒ t > 0.5
Combined: 0.5 < t < 1.5, i.e., t ∈ (1/2, 3/2). Answer: (C).
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