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GATE CE 2015 Set 1 — Question 61

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NAT+2 / -0HardMicroscopic ParametersTraffic Studies & FlowTransportation EngineeringFirst-Order Linear EquationsOrdinary Differential EquationsEngineering Mathematics

Engineering Mathematics → Ordinary Differential Equations → First-Order Linear Equations

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Question

The acceleration-time relationship for a vehicle subjected to non-uniform acceleration is,dvdt=(α−βv0)e−βt\frac{dv}{dt} = (\alpha - \beta v_0)e^{-\beta t}where, vv is the speed in m/s, tt is the time in s, α\alpha and β\beta are parameters, and v0v_0 is the initial speed in m/s. If the accelerating behavior of a vehicle, whose driver intends to overtake a slow moving vehicle ahead, is described as,dvdt=(α−βv)\frac{dv}{dt} = (\alpha - \beta v)Considering α=2 m/s2\alpha = 2 \text{ m/s}^2, β=0.05 s−1\beta = 0.05 \text{ s}^{-1} and dvdt=1.3 m/s2\frac{dv}{dt} = 1.3 \text{ m/s}^2 at t=3 st = 3 \text{ s}, the distance (in m) travelled by the vehicle in 35 s is _______________.
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