QQuestionPhysics
QuestionPhysics
Stopping distances and severity of crashes:
A. Increase as vehicle speed increases
B. Are not affected by vehicle speed
C. Decrease as vehicle speed increases
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understanding Stopping Distance
Stopping distance is the total distance a vehicle travels from the moment a driver perceives a hazard until the vehicle comes to a complete stop. This involves two key components: - Reaction distance (time to recognize and start braking) - Braking distance (actual distance traveled while braking)
Step 3:: Relationship Between Speed and Stopping Distance
The stopping distance is directly related to the vehicle's speed. As speed increases, the stopping distance increases exponentially, not linearly.
Step 4:: Physics Behind Stopping Distance
As velocity ($$v$$) increases, kinetic energy increases quadratically.
The relationship can be explained by the kinetic energy formula: This means: - Doubling speed quadruples kinetic energy - More energy must be dissipated during braking - Longer stopping distances result
Step 5:: Mathematical Verification
- At 90 mph, stopping distance would be $$9x
This means:
Step 6:: Crash Severity
Higher speeds also increase crash severity because: - More kinetic energy is transferred during collision - Greater force of impact - Less time to react and avoid collision
Final Answer
Stopping distances and crash severity increase as vehicle speed increases.
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