A particle starts from rest and travels along a straight line with an accelerati

Question

A particle starts from rest and travels along a straight line with an acceleration a=(30-0.2v)ft/s^2 where v is in ft/s.

Determine the time when the velocity of the particle is v=80ft/s

Explanation / Answer

a = (30 - 0.2v) ft/s^2 dv/dt = 30 - 0.2v =>dv/(30 - 0.2v) = dt integrating both sides we get ln(30 - 0.2v)/-0.2 = t + c/-0.2 ln(30 - 0.2v) = -0.2t + C v = 0 at t = 0 (given that particle starts from rest) so, ln30 = 0 + c =>c = ln30 = ln30 =>ln(30 - 0.2v) = -0.2t + ln30 when v = 80 ft/s ln(30 - 0.2*80) = -0.2t + ln30 =>ln14 = -0.2t + ln30 =>0.2t = ln30 - ln14 =>t = 5(ln30 - ln14) = 3.81 s

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