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A toy car is moving on a closed track wh...

A toy car is moving on a closed track whose curved portions are semicircles of radius `1m`. The adjacent graph describes the variation of speed of the car with distance moved by it (starting from point `P`). The time `t` required for the car to complete one lap is equal to `6k` second. Find `k` (take `piln2~~2`)

Text Solution

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For the motion from `A` to `B`
applying `s=vt`,
`2=0.25 t_(AB)`
`t_(AB)=8`
For the motion from `B` to `C`
`-(dv)/(dl)=(0.125)/((pi)/(2))=(1)/(4pi)=-(dv)/(dl)xx(dt)/(dt)`
`int_(0)^(t_(BC))(dt)/(4pi)=int_(0.25)^(0.125)-(dv)/(v)`
`rArr t_(BC)=4piln2`
`t_(BC)=t_(CD)=t_(EF)=t_(FG)`
`t_(AB)=t_(DE)`
total time will be sum of all times `=16(1+piln2)`
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