A scooter can produce a maximum acceleration of `5m s^(-2)`. Its brakes can produce a maximum retardation of `10 "ms"^(-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=2xx5xxS_1 rArr S_1 =v^2/10` ,
Also during retardation
`o^2-v^2=2xx10xxS_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=(1500xx20)/3 =1000` or `v=100 ms^(-1)`
`v = alpha t_1 rArr t_1=100/5`=20 sec
`v=betat_2 rArr t_2=100/10` = 10 sec
Total time =20+10 =30 sec.