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A particle starts with initial speed u and retardation a to come to rest in time t . The time taken to cover first half of the total path travelled is . Please explain properly

A particle starts with initial speed u and retardation a to come to rest in time t . The time taken to cover first half of the total path travelled is . Please explain properly

Grade:11

1 Answers

Nicho priyatham
625 Points
8 years ago
while solving 1 diminsion  problems in kinamitcs 
u have to remember 3 important equations 
s=ut+(1/2)at2=vt-(1/2)at2 …......(1)
v=u+at..........(2)
v2-u2=2as........(3)
now coming to problem
u=u 
v=0
a=-a(retardation)
  • by apply second equation above we get
            0=u-at so u=at............(3)
  • now apply first equation  and substuting eq 3
         s=(1/2)at2 =(1/2)ut …........(4)
  • now say partical takes T seconds to cover s/2 applying eq 1 again and sudstuting eq 4
                      s/2=uT-(1/2)aT2
                               1/4ut=uT-(1/2)(u/t)T2
                                solving the above equation we get the quaratic 
                                2T2 -4tT+t2=0
  solving the above equation we get 
T=(1-(1/(root2))t or (1+(1/(root2))t (reject as greater than t)
so T=(1-(1/(root2))t 
PLEASE APROOVE
 

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