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Like to solve the following problem?

Narasimhan M K
03/11/2016 0 0

Consider the following :

A particle moves along a straight line as per law:Power is proportional to displacement raised to power  -3/2. That is,PS-3/2.Then, acceleration is proportional to which power of velocity?

Solution:(usual method) P=Fv=mav= m(dv/dt)v=m(dv/ds)(ds/dt)v=m(dv/ds)v2 

given:PS-3/2 ⇒(dv/ds)v2=S-3/2

Integrating,v3s-1/2 .   v s-1/6. Therefore,a(s-3/2)/v =(v-9)/v =v8 

Hence,Answer is  , acceleration is proportional to 8th power of velocity.

An easier and general method for such problems:Let s∝tn

then,v∝tn-1  and a∝tn-2  

Hence av∝s-3/2 means tn-1 tn-2 =t-3n/2 ⇒n=6/7,a∝t-8/7 and v∝t-1/7 and hence a∝v8

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