An old person moves on a semi circulasr track of radius 40.0 m during a moirning walk. If he starts at one end of the track and reaches at the other end, find the distance covered and the displacement of the person.

Explanation

By substituting the given equation in equation `a=dv//dt`, we have
`dv=(3-2t)dt rArr underset(v_(o))overset(v)(int)dv=underset(0)overset(t)(int)(3-2t)dtrArr v=v_(o)+3t-t^(2)` …(i)
By substituting eq. (i) in equation `v=dx//dt`, we have
`dx=(v_(o)+3t-t^(2))dt rArr underset(x_(o))overset(x)(int) dx=underset(0)overset(t)(int)(v_(o)+3t-t^(2))dt rArr x=x_(o)+v_(o)t+3/2 t^(2)-1/3 t^(3)` ...(ii)
(a) applying the given condition that the particle occupies the same x coordinate at the instant `t=0` and `t=6s` in eq. (ii), we have
`x_(o)=x_(6)rArr x_(o)=x_(o)+6v_(o)+54-72rArr v_(o)=3m//s`
(b) Using `v_(o)` in eq. (i), we have `v=3+3t-t^(2)rArr v_(2)=5m//s`