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Answer :
Final answer:
Honda's car will not pass its brake examination test because its actual deceleration of -3.0376 m/s² is less than the required 4.23 m/s². Additionally, the provided duration of 215 seconds to stop is unrealistic and likely a typo.
Explanation:
To determine if Honda's car will pass its brake examination test, let's calculate the car's actual deceleration. Based on the provided information, we need to check if the car can decelerate with an acceleration of at least 4.23 m/s2. Given that the Honda car travels a distance of 25 meters and was originally traveling at a speed of 17.4 m/s, we can use the kinematic equation:
v2 = u2 + 2as,
where:
- v is the final velocity (0 m/s since the car stops).
- u is the initial velocity (17.4 m/s).
- a is the acceleration (which is a deceleration in this case).
- s is the distance (25 meters).
Rearranging for a gives us:
a = (v2 - u2) / (2s)
a = (0 - 17.42) / (2 * 25)
a = -151.88 / 50
a = -3.0376 m/s2
The negative sign indicates deceleration. The deceleration of the Honda car, -3.0376 m/s2, is less than the required 4.23 m/s2. Hence, Honda's car will not pass its brake examination test.
Additionally, there appears to be an error with the duration provided as 215 seconds for the car to come to a stop, which seems unrealistically long, so we are assuming it's a typo and not factored into calculations.
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