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# what is ratio of average velocity to maximum velocity

Asked by Prashant DIGHE 10th July 2019, 1:53 PM
Let t1 be the initial time duration when the particle is under accelerated motion.

Distance S travelled in t1 seconds = (1/2)a×t12  .......................(1)

where a is acceleration. If v is the velocity after t1 seconds, then,  v = a×t1 ..............(2)

hence using eqn.(2), Distance S travelled in t1 seconds is given by,

S = (1/2)v×t1   or   t1 = 2S/v  ...................(3)

If distance 2S is travelled with uniform velocity v, time duration t2 = 2S/v  ......................(4)

If distance 3S is travelled with retardataion ar in t3 seconds,

then we have,  3S = v×t3 - (1/2)×ar×t32 .................(5)

Retardation ar  and t3 are related as, v = ar × t3  ....................... (6)

using eqn.(6) in eqn.(5), we get,  3S = (1/2)v×t3   or  t3 = 6S/v

Displacement = S+2S+3S = 6S  ;  total time = t1 + t2 + t3 = ( 2S/v ) + ( 2S/v ) + ( 6S/v ) = ( 10S/v )

average velocity = Displacement/totalTime = 6S / ( 10S/v) = (3/5)v

since maximum velocity is v, ratio of average velocity to maximum velocity = (3/5)
Answered by Expert 10th July 2019, 3:45 PM
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