In the typical model of solid particle motion in a viscous fluid it is assumed that the particle
deceleration is proportional to the particle speed. Recall what is the mathematical definition of
acceleration/deceleration and how it relates to speed u(t).
a) Translate the statement about particle motion into a mathematical equation and introduce
a coefficient of proportionality k. [5 marks]
b) Assume that at the initial instant of time the particle speed was 10 m/s; and after eight
minutes the speed becomes 1 m/s. Find the particular solution of the differential equation
derived in item (a) subject to the initial condition and determine all unknown constants.
Present the particular solution in the explicit form. [7 marks]
c) Find at what time the particle speed drops to 1/100 of its initial value? Present your
answer in seconds and minutes.