The rate at which the remainder of a substance dissolves in a small quantity of water is inversely proportional to the weight, w grams of the substance already dissolvod. Initially, there are 20 grams of the undissolved substance. Show that after Lime t scoonds, the eitestirn can be modelled by the difforential cquation (a) (20-w)= dt where k is a positive constant. Afler I second, 6 grams of the substance have disolved. Show that w- 36t Hence , find (0) (1) the weight of the substance remaining undissolved after 4 seconds. (ii) the time taken for 18 grams of the substance lo be dissolved.
The rate at which the remainder of a substance dissolves in a small quantity of water is inversely proportional to the weight, w grams of the substance already dissolvod. Initially, there are 20 grams of the undissolved substance. Show that after Lime t scoonds, the eitestirn can be modelled by the difforential cquation (a) (20-w)= dt where k is a positive constant. Afler I second, 6 grams of the substance have disolved. Show that w- 36t Hence , find (0) (1) the weight of the substance remaining undissolved after 4 seconds. (ii) the time taken for 18 grams of the substance lo be dissolved.
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:The rate at which the remainder of a substance dissolves in a small quantity of water is inversely
proportional to the weight, w grams of the substance already dissolved. Initially, there arc 20 grams
of the undissolved substance. Show that after lime t scoonds, the sinetinn can be modelled by the
differential equation
3.
(a)
-k
(20- w)=
dt
where k is a positive constant.
Afler I second, 6 grams of the substance have dissolved.
Show (hat w-36t
Hence, find
(1)
the weight of the substance remaining undissolved after 4 seconds.
(i)
the time taken for 18 grams of the substance to be dissolved.
(L)
A prarticle performs simple harmonic motion btween two points A and B which are 10 metres apart
on a horizontal straight line. Whcn the particle is 3 metres away from the centre, O, of the line AB,
its spced is 8ms'.
Find
(1)
the periodie time of the motion.
(ii)
the least timo required for the particle to move from B to the midpoint of OA.
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