You are driving along the New York State Thruway in a line of cars all travelling at a constant speed of 108.5 km/hr. The car in front of you applies its brakes for maximum acceleration. You then apply your brakes to achieve the same maximum acceleration after only a 1 s delay due to reaction time. What distance behind the car in front of you must you be to avoid a collision?

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CarliReifsteck CarliReifsteck · Answer 1 · 2020-09-09T13:25:46+02:00

Answer:

Car first should be 30.13 m behind the second car.

Explanation:

Given that,

Constant speed = 108.5 Km/hr

Time = 1 sec

Let the distance covered by second car S and by first car S'

We need to calculate the distance covered by second car

Using equation of motion

[tex]S=ut-\dfrac{1}{2}at^2[/tex].....(I)

The distance covered by first car to avoid collision

[tex]S''=S'+S[/tex]

Put the value into the formula

[tex]S'+S=ut+ut-\dfrac{1}{2}at^2[/tex]...(II)

We need to calculate the distance covered by first car

Using equation (I) and (II)

[tex]S'=ut[/tex]

Put the value into the formula

[tex]S'=108.5\times\dfrac{5}{18}\times1[/tex]

[tex]S'=30.13\ m[/tex]

Hence, Car first should be 30.13 m behind the second car.