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Elasticity question

Question:
A load of 31.4 kg is suspended from a wire of radius 10-3m and density 9103Kg/m3. Calculate the change in the temperature of the wire if 75% of the work done is converted into heat. The Young’s modulus and the heat capacity of the material of the wire are 9.81010Nm-1and 490 J/KgK respectively.
Solution

How to solve problems involving time dependent acceleration

Here i tried to sum up the steps to solve problems involving time dependent acceleration. We can easily calculate the position of the particle/object
(1) Consider that acceleration a is some function of time such that
a=f(t)
this equation can also be written in terms of velocity i.e.
a=dv/dt=f(t)                                        .....1
(2) Now we integrate equation 1 as a function of time
dv=f(t)dt
v=∫dv=∫f(t)dt + C                ......2
here C is some constant of integration and can be calculated from the initial conditions.
(3) Now we know that v=dx/dt , using this in the solution of equation 2 we can easily find position of the particle.