A car is moving with speed `20 m//s`. Suddenly the driver sees the sign of danger at a distance of `50 m`, after a certain reaction time `t_(0)`, he applies breaks to cause deceleration `5 m//s^(2)`. What is the maximum allowable reaction time `t_(0)` to avoid accident and distance traveled by the car during reaction time?

Explanation

`v^(2)=u^(2)-2as`
`0=(20)^(2)-2xx5d_(2) implies d_(2)=40 m`
`d_(1)+d_(2)=50`
`20 t_(0)+40=50 implies t_(0)=0.55 s`
`d_(1)=20 t_(0)=10 m`