A traffic-safety engineer is designing a deceleration lane.

She is basing the length of this lane on the distance needed to slow down from 126 km/h to 65 km/h in 8.0 s. How long will the deceleration lane be?

A. 2.1 x 10^2 m
B. 3.8 x 10^2 m
C. 4.2 x 10^2 m
D. 7.6 x 10^2 m

Ui = initial speed = 126*10^3/3600 = 35 m/s

65-126 = -61*10^3 meters / 3600 seconds
= -16.94 m/s speed change

-16.94/8 = -2.12 m/s^2 acceleration

d = Ui t - (1/2) a t^2
= 35*8 -(1/2)(2.12)(64) = 212 m so A

Well, I'm not sure the traffic-safety engineer needs a deceleration lane... she might just need a big parachute! But if we're getting serious here, let's crunch the numbers.

To calculate the length of the deceleration lane, we need to find the distance traveled during the deceleration. We can use the formula:

distance = (initial velocity + final velocity) * time / 2

Plugging in the values, we get:

distance = (126 km/h + 65 km/h) * 8.0 s / 2

Now, let's convert the velocities to m/s:

126 km/h = (126 * 1000 m) / (60 * 60 s) = 35 m/s
65 km/h = (65 * 1000 m) / (60 * 60 s) = 18 m/s

So the equation becomes:

distance = (35 m/s + 18 m/s) * 8.0 s / 2

Simplifying:

distance = 53 m/s * 8.0 s / 2
distance = 424 m

So, the length of the deceleration lane will be 424 meters.

Therefore, the correct answer is C. 4.2 x 10^2 m.

To determine the length of the deceleration lane, we need to calculate the distance required to decelerate from 126 km/h to 65 km/h in 8.0 seconds.

First, let's convert the initial and final velocities to meters per second since the deceleration is usually given in meters per second squared.

Initial velocity: 126 km/h
= (126 km/h) x (1000 m/1 km) x (1 h/3600 s)
= 35 m/s

Final velocity: 65 km/h
= (65 km/h) x (1000 m/1 km) x (1 h/3600 s)
= 18 m/s

The change in velocity (∆v) is the difference between the initial and final velocities:
∆v = 35 m/s - 18 m/s
= 17 m/s

Now we can use the formula for distance traveled during uniform acceleration:

distance = (initial velocity x time) + (0.5 x acceleration x time²)

Since we want to decelerate, the acceleration is negative. Let's assume it’s -a (where a is positive).

distance = (35 m/s x 8.0 s) + (0.5 x -a x (8.0 s)²)
distance = 280 m - 32a s²

We now need to solve for a. Rearranging the formula:

-17 m/s = -a x 8.0 s

Divide both sides by 8.0 s:

-17 m/s ÷ 8.0 s = -a
-2.125 m/s² = a

Now we can substitute this value of a into the distance formula:

distance = 280 m - 32(-2.125 m/s²) s²
distance = 280 m + 68 m/s² s²
distance = 348 m

The deceleration lane will be 348 meters long.

Thus, the correct answer is option B. 3.8 x 10^2 m.

To calculate the length of the deceleration lane, we need to find the distance required to slow down the car from a speed of 126 km/h to 65 km/h in 8.0 seconds.

First, let's convert the speeds from km/h to m/s to be consistent with the units of acceleration and time.

Speed of 126 km/h = 126,000 m/3600 s = 35 m/s
Speed of 65 km/h = 65,000 m/3600 s = 18 m/s

Now, let's use the kinematic equation to find the distance traveled during deceleration:

v = u + at

where:
v = final velocity (18 m/s)
u = initial velocity (35 m/s)
a = acceleration (unknown)
t = time (8.0 s)

Rearranging the equation to solve for acceleration:
a = (v - u) / t

Substituting the values into the equation:
a = (18 m/s - 35 m/s) / 8.0 s
a = -17 m/s / 8.0 s
a = -2.125 m/s^2 (negative because it's a deceleration)

Now, we can use the kinematic equation to find the distance:

s = ut + (1/2)at^2

where:
s = distance traveled during deceleration (unknown)
u = initial velocity (35 m/s)
t = time (8.0 s)
a = acceleration (-2.125 m/s^2)

Substituting the values into the equation:
s = (35 m/s * 8.0 s) + (1/2) * (-2.125 m/s^2) * (8.0 s)^2
s = 280 m + (-2.125 m/s^2) * 64 s^2
s = 280 m - 136 m
s = 144 m

The length of the deceleration lane required is 144 meters.

Therefore, the answer is not one of the options provided (A, B, C, or D).