Question

A car, velocity +35 m/s, slows down at a rate of -8.5 m/s² to a stop on a dry road. The same car traveling at +35 m/s slows down at a rate of -6.5 m/s² to a stop on a wet road. How much farther does the car travel on the wet road before coming to a stop?

Answer 1

Using the motion equation, the car travels 115.17 meters farther on the wet road before stopping compared to the dry road due to the lower deceleration rate.

Step-by-step explanation:

To determine how much farther a car travels on a wet road before coming to a stop compared to a dry road, we use the equation for motion with constant acceleration:
s = vt - ½at², where s is displacement, v is initial velocity, a is acceleration, and t is time.

Firstly, for a dry road:

• Initial velocity v = +35 m/s
• Acceleration a = -8.5 m/s² (deceleration)
• Final velocity = 0 m/s (coming to a stop)

Using the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is acceleration, and s is displacement, we can solve for s:

0 = (35)² + 2(-8.5)s

Displacement on dry road, s dry = 72.06 m

Secondly, for a wet road:

• Initial velocity v = +35 m/s
• Acceleration a = -6.5 m/s² (deceleration)
• Final velocity = 0 m/s (coming to a stop)

0 = (35)² + 2(-6.5)s

Displacement on wet road, s wet = 187.23 m

The car travels farther on the wet road before coming to a stop. To find the additional distance traveled on a wet road, we subtract the dry road displacement from the wet road displacement: 187.23 m - 72.06 m = 115.17 m

Conclusion: The car travels 115.17 meters farther on the wet road before coming to a stop compared to the dry road.