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A scooter can produce a maximum accelera...

A scooter can produce a maximum acceleration of `5ms^(-2)`. It brakes can produce a maximum retardation of `10ms^(-2)`. The minimum time in which it can cover a distance of 1.5km is?

Text Solution

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If v is the maximum velocity attained,
then during acceleration is between A, B
`v^(2)-o^(2)=2xx5xxS_(1)impliesS_(1)=(v^(2))/(10)`,
Also, during retardation
`o^(2)-v^(2)=2xx10xxS_(2)impliesS_(2)=(v^(2))/(20)`
`S=S_(1)+S_(2)implies1500=(v^(2))/(10)+(v^(2))/(20)=(3v^(2))/(20)or`
`v^(2)=(1500xx20)/(3)=10000 or v=100ms^(-1)`
`v=alphat_(1)impliest_(1)=(100)/(5)=20sec`
`v=betat_(2)impliest_(2)=(100)/(10)=10sec`
Total time `=20+10=30sec`.
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