(a) When an object falls from rest at t = 0 through a resisting liquid. the rate of change dv of its velocity at time t is given by = -k(v – 600), where k is a positive constant. dt (i) Show that v = 600 + Pe-kt is a solution to the differential equation for some constant P. (ii) If the velocity of the object at t = 3s is 25 ms-1, find P and k. (iii) Find the velocity of the object at t = 10s. Give your answer correct to one decimal place. (iv) What is the limiting value of v as t - x?
(a) When an object falls from rest at t = 0 through a resisting liquid. the rate of change dv of its velocity at time t is given by = -k(v – 600), where k is a positive constant. dt (i) Show that v = 600 + Pe-kt is a solution to the differential equation for some constant P. (ii) If the velocity of the object at t = 3s is 25 ms-1, find P and k. (iii) Find the velocity of the object at t = 10s. Give your answer correct to one decimal place. (iv) What is the limiting value of v as t - x?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2)
(a) When an object falls from rest at t = 0 through a resisting liquid. the rate of change
dv
of its velocity at time t is given by
= -k(v – 600), where k is a positive constant.
dt
%3D
(i) Show that v = 600 + Pe¬kt is a solution to the differential equation for some
constant P.
(ii) If the velocity of the object at t = 3s is 25 ms-1, find P and k.
(iii) Find the velocity of the object at t = 10s. Give your answer correct to one
decimal place.
(iv) What is the limiting value of v as t – x?
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