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A motorist traveling at 17 m/s encounters a deer in the road 46 m ahead. If the maximum acceleration the vehicle’s brakes are capable of is −6 m/s 2 , what is the maximum reaction time of the motorist that will allow her or him to avoid hitting the deer? Answer in units of s.

Respuesta :

Answer:

[tex]t = 1.29 s[/tex]

Explanation:

Maximum distance after which the motorist must have to stop is given as

[tex]d = 46 m[/tex]

now the distance after which the vehicle will stop on applying breaks is given as

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

[tex]0 - 17^2 = 2(-6) d[/tex]

[tex]d = 24.1 m[/tex]

now remaining distance is given as

[tex]x = 46 - 24.1[/tex]

[tex]x = 21.9 m[/tex]

now reaction time is given as

[tex]t = \frac{x}{v}[/tex]

[tex]t = \frac{21.9}{17}[/tex]

[tex]t = 1.29 s[/tex]

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