A particle moves along a straight line with acceleration given by a = 32 - 4v (in SI units). At time t = 0 the velocity is v = 4 m/s. Find the velocity of the particle at t = ln(2) seconds.

15/2
17/2
23/4
31/4

Correct answer: 31/4

Solution

Solving dv/(32-4v) = dt gives v(t) = 8 - 4*e^(-4t). At t = ln2, e^(-4*ln2) = 2^(-4) = 1/16, so v = 8 - 4/16 = 8 - 1/4 = 31/4.

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