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

Explanation

If v is the maximum velocity attained, then during acceleration ie between A,B
`v^(2)-o^(2)=2 xx 5 xx S_(1) rArr S_(1)=v^(2)/(10)`,
Also, during retardation
`o^(2)-v^(2)=2 xx 10 xx S_(2) rArr S_(2)=(v^(2))/(20)`
`S=S_(1)+S_(2) rArr 1500 =(v^(2))/(10)+v^(2)/(20)=(3v^(2))/(20) or v^(2)=(1500 xx 20)/(3)=10000 or v=100ms^(-1)`
`v=alphat_(1) rArr t_(1)=(100)/(5)=20 sec`
`v=beta t_(2) rArr t_(2)=(100)/(10)=10 sec`
`v=beta t_(2) rArr t_(2)=(100)/(10)=10sec`
Total time =20+10=30sec.