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A car starting from rest accelerates at ...

A car starting from rest accelerates at the rate f through a distance S, then continues at a constant speed for time t and then decelerates at rate f/2 to come to rest. If the total distance travelled is 15 S, then

Text Solution

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Let constant speed be `v_(m)`
for time `t_(1), v_(m)= ft_(1) and S=(1)/(2)ft_(1)^(2)`
for time, `t_(2) O=v_(m) -(f)(2) t_(2)rArr t_(1)=2t_(1)`
`S-(3)=(1)/(2)((f)/(2))t_(2)^(2)=((f)/(4))(4t_(1)^(2)) =ft_(1)^(2)=2S`
Therefore `S+v_(m)t+2S=15SrArrv_(m)t=12SrArr ft_(1)t=12S`
`rArrf((2S)/(f))^(1//2)t=12S rArr 2Sf= (144S^(2))/(t^(2)) rArr S=(ft^(2))/(72)`
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