The driver of a car moving at `30 ms(-1)` suddenly sees a truck that is moving in the same direction at `10 ms^(-1)` and is `60 m` head. The maximum deceletation of the car is `5 ms(-2)`.
a. Will the collision occur if the driver's reaction time is zero ? If so. then?
b. If the car driver's reaction time of `0.5 s` included, what is the minimum deceleration required to avoied the collision?.

Answer

`4 m s^(-2)`

Explanation

a. Let collision occurs at time `t`. For car w.r.t. tuck: `S_(rel)=urel t +(1)/(2) a_(rel t^(2)`
`rArr 60=(30-10) (t_(1))/(2) (-5-0)t^(2)`
rArr `t^(2)-8t+24=0`, from here we will get no real value of `t`, it means collision does not occur.
b. Relative distance coveredin`0. 5 s=(30-10) 0. 5 =10 m`,
`50 =(30 =10)t +(1)/(2)(-a-0)t^(2)`
`rArr at^(2)-40 t +100=0`
To avoid collision, itsdiscriminant `D l e 0`
`rArr 40^(2)-4a 100 g e 0` rArr a l e 4 m s^(-2)`.