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a particle moves along x axis with acceleration a = a(0)[1-t/T] where a(0) and T are constantsif velocity at t=0 is zero then find the average velocity from t=0 to the time when a=0

a particle moves along x axis with acceleration a = a(0)[1-t/T] where a(0) and T are constantsif velocity at t=0 is zero then find the average velocity from t=0 to the time when a=0

Grade:11

1 Answers

Nicho priyatham
625 Points
8 years ago
time wn a=0 is t=T
so u need to find  vavg in intevral t=0 to t=T
so vavg=(dist covered)/T
now find distance covered
on integration v=∫a(t)dt
     v=∫a(0)(1-(t/T))dt  (take limits from 0 to v on LHS and o to t on RHS)
       =a(0)(t-(t)2/2T)  
      s=∫vdt                   
        =∫a(0)(t-(t)2/2T)dt   
        =a(0)(t2/2-t3/6T)       (take limits from 0 to s on LHS and o to T on RHS)
        =a(0)(T2/2-T3/6T)
           =a(0)T2/3
so now vavg= s/T
                     =a(0)T/3 
PLZ APPROVE  IF USEFUL and in case of further doubts ask in ans box

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