You’re driving down the highway late one night at 20m/s when a deer steps onto the road 85m in front of you. Your reaction time before stepping on the brakes is 0.50s, and the maximum deceleration of your car is 9m/s2. From the time you first see the deer until your car comes to a complete stop, how far have you travelled?

The car travels to a complete stop from the time the deer is first seen and the distance traveled is 10.04 m.

Explanation:

The speed of the car is 20 m/s.

The deer that steps on to the road is 85 m in front of the car.

Seeing the deer the brakes are applied but after a reaction time of 0.5 seconds.

The deceleration of the car is given as 9 m/.

The formula for distance is given as

   ....    (i)

where s  = distance traveled in meters

           u = initial velocity

           a = acceleration

           t = time

and v = u + at   ....     (ii)

where v  = final velocity

           u = initial velocity

           a = acceleration

           t = time in seconds

Therefore we have from (ii)  0 = 20 - 9t

Therefore time it takes for the car to stop, t = = 2.22 seconds.

Therefore from (i) we have

s = 20(t + 0.5)  - 9

  = 20(2.22 + 0.5) - (9 × )

   = 54.4  - 44.36

   = 10.04 m

In the above distance formula that is also mentioned in (i) we have accounted for the reaction time which is 0.5 seconds.

The car travels to a complete stop from the time the deer is first seen and the distance traveled is 10.04 m.

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force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach