A driver is driving a car at a speed of 90km/h. he spots a child standing on his way and decided to apply the brakes but it took him 0.3s to actually apply the brakes. If the retardation produced by the brakes is `10m//s^(2)`, calcualtion the total distance covered by car before coming to rest

Explanation

Speed of the car (u)=90km/h
`=90xx(5)/(18)m//s=25m//s`
The driver took 0.3 s to react. Hence, the car continues to move with constant speed of 25m/s for 0.3s. Distance travelled by the car during this interval of time
`x_(1)=25m//sxx0.3s=7.5m`
For constant retardation, we can use the following equation:
`v^(2)=u^(2)+2as`
`rArr (0)^(2)=(25)^(2)+2(-10)x_(2)`
`rArr x_(2)=((25)^(2))/(20)=(625)/(20)=31.25m`
Total distance travelled by the car before it comes to rest can be written as follows:
`x=x_(1)+x_(2)=7.5+31.25=38.75m`.