A praricle performs simple harmonic motiou biween two points A and B which are 10 metres apart on a horizontal straight line. Whecn the particle is 3 metres away from the centre, O, of the line AB, its spced is 8ms'. Find (1) the periodic time of the motion. (ii) the least timo required for the particle to move from B to the midpuint of OA.

University Physics Volume 2
18th Edition
ISBN:9781938168161
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Chapter2: The Kinetic Theory Of Gases
Section: Chapter Questions
Problem 97CP: Verify the normalization equation 0f(v)dv=1 In doing the integral, first make substitution...
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Answer Q3b

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.
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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