PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A speed-boat of mass 500kg moves on still water. Its engine delivers a constant power of 45kW. The boat experiences a resistive drag force given by Fd=150v2, where v is the instantaneous speed in ms−1 and Fd in newtons.
(i) Show that the boat approaches a maximum (terminal) speed and determine the numerical value of this speed.
(ii) Establish the differential equation governing the variation of speed with time when the boat starts from rest, and obtain an expression for the time t required for the speed to reach one-half of the terminal value.
(iii) Evaluate the time calculated in part (ii).