A boat's engine is cut at

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Calculus of change and accumulation · Calculus of change and accumulation

Mathematical Methods for Physics, Ch Accumulation: integration and the techniques that make it possible

Problem

A boat's engine is cut at t=0t=0, after which drag slows it so that its speed falls as v(t)=v0(1+t/τ)2,v(t) = \frac{v_0}{\left(1+t/\tau\right)^2}, with v0=15 m s−1v_0 = 15\,\text{m s}^{-1} and τ=8.0 s\tau = 8.0\,\text{s}. Water resistance is the only force considered. ((a)) Write the distance travelled between t=0t=0 and a finite time TT as a definite integral, and evaluate it. ((b)) Take T→∞T \to \infty to find the total distance travelled before the boat stops, stating this as the limit that defines the improper integral.

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