A motorcycle rider travelling at 30m/s sees a child run into the streets 190m ahead. If the rider takes 1 second to react before beginning to decelerate at a rate of 3m/s^2, does he stop in time, and if so by what distance is the child safe? (Hint: there a 2 stages of motion)

The distance by which the child is safe is  

Explanation:

From the question we are told that

  The speed of the motorcycle is  

   The distance of the child from the motorcycle is L =  190 m

    The reaction time is  

    deceleration is  

Generally the distance covered during the reaction time is  

=>

=>

Generally the distance covered during the deceleration

Here v is the final velocity which is  zero  

So

=>

So the total distance the motorcycle rider will cover before coming to rest is  

=>  

=>  

Therefore the amount of distance by which the child id safe is  

=>

=>