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A motorist traveling at 17 m/s encounters a deer in the road 39 m ahead. If the maximum acceleration the vehicle’s brakes are capable of is
Question
A motorist traveling at 17 m/s encounters a deer in the road 39 m ahead. If the maximum acceleration the vehicle’s brakes are capable of is −7 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. 019 (part 2 of 2) 10.0 points If his or her reaction time is 1.21983 s, how fast will (s) he be traveling when (s)he reaches the deer? Answer in units of m/s.
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Physics
3 years
2021-07-19T00:17:04+00:00
2021-07-19T00:17:04+00:00 1 Answers
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Answers ( )
Answer:
1. t_reaction = 1.08 s
2. v₀₁ = 16.365 m/s
Explanation:
1. This is a kinematics exercise, let’s analyze the situation a bit, we can calculate the braking distance and the rest of the distance we can use to calculate the reaction time.
Braking distance
v² = v₀² + 2 a x
when he finishes braking the speed is v = 0
0 = v₀² + 2 a x
x = -v₀² / 2a
x = – 17²/2 (-7)
x = 20.64 m
the distance for the reaction is
d = x_reaction + x
x_reaction = d – x
x_reaction = 39 – 20.64
x_reaction = 18.36 m
as long as it has not reacted the vehicle speed is constant
v = x_reaction / t_reaction
t_reaction = x_reaction / v
t_reaction = 18.36 / 17
t_reaction = 1.08 s
2. Let’s find the distance traveled in the reaction time of t1 = 1.21983 s
as the speed is constant
v = x / t
x₁ = v t₁
the distance traveled during braking is
v² = v₀² + 2a x₂
0 = v₀² + 2 a x₂
x₂ = -v₀² / 2a
v = v₀
the total distance is
x_total = x₁ + x₂
x_total = v₀ t₁ + v₀² / 2a
39 = v₀ 1.21983 + v₀²/14
v₀² + 17.08 vo – 546 =0
we solve the second degree equation
v₀ = [ -17.08 ±√(17.08² + 4 546) ]/2
v₀ = [-17.08 ± 49.81 ]/2
v₀₁ = 16.365 m/s
v₀₂ = – 33.445 m/s
as the acceleration is negative the correct result is v₀₁ = 16.365 m/s