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?

A scooter can produce a maximum acceleration of 5ms^(-2).Its brakes ca

1.	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?
Answer» Solution : 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.