GATE Civil Engineering (CE) 2015 Shift 1 Solved Paper

The acceleration-time relationship for a vehicle subjected to non-uniform acceleration is,
$\frac{\mathit{d}\mathit{v}}{\mathit{d}\mathit{t}}=\left(\mathit{\alpha }-\mathit{\beta }{\mathit{v}}_0\right){\mathit{e}}^{-\mathit{\beta }\mathit{t}}$
where, v is the speed in m/s, t is the time in s, α and β are parameters, and v0 is the initial speed in m/s. If the accelerating behaviour of a vehicle, whose driver intends to overtake a slow moving vehicle ahead, is described as,
$\frac{\mathit{d}\mathit{v}}{\mathit{d}\mathit{t}}=\left(\mathit{\alpha }-\mathit{\beta }\mathit{v}\right)$
Considering α = 2 m/sec², β = 0.05 s^-1 and $\frac{\mathit{d}\mathit{v}}{\mathit{d}\mathit{t}}=1.3\mathit{m}∕{\mathit{s}}^2$ at t = 3 s, the distance (in m) travelled by the vehicle in 35 s is ___. m