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A woman is driving her truck with speed 53.0 mi/h on a horizontal stretch of road.

(a) When the road is wet, the coefficient of static friction between the road and the tires is 0.104. Find the minimum stopping distance (in m).

User Akatum
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1 Answer

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Final answer:

To find the minimum stopping distance on a wet road for a truck traveling at 53.0 mi/h, convert the speed to m/s, use the coefficient of static friction to calculate deceleration, and then apply the kinematic equation. The minimum stopping distance is approximately 276.3 meters.

Step-by-step explanation:

To calculate the minimum stopping distance on a wet road for a woman driving her truck at 53.0 mi/h, we first need to convert the speed to meters per second (m/s). Since 1 mile is approximately 1.60934 kilometers and 1 hour is 3600 seconds, we can convert the speed as follows:

53.0 mi/h × (1.60934 km/mi) × (1000 m/km) ÷ (3600 s/h) ≈ 23.7 m/s.

Now, using the coefficient of static friction (μ) and the acceleration due to gravity (g ≈ 9.8 m/s²), the maximum deceleration (a) on wet concrete can be calculated through the equation a = μ × g, giving us:

a = 0.104 × 9.8 m/s² ≈ 1.0192 m/s².

Applying the kinematic equation for stopping distance (d), which is d = v²/(2a), where v is the initial velocity and a is the deceleration:

d = (23.7 m/s)² / (2 × 1.0192 m/s²) ≈ 276.3 m.

Therefore, the minimum stopping distance on a wet road for the truck traveling at 53.0 mi/h is approximately 276.3 meters.

User Carine
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