Concept explainers
(a)
Minimum negative acceleration to avoid collision.
(a)
Answer to Problem 88P
Minimum negative acceleration to avoid collision is
Explanation of Solution
Given:
Velocity of passenger train is
Separation between passenger and freight train when engineer sees it is
Velocity of freight train is
Reaction time of engineer is
Formula used:
Write the expression for relative velocity.
Here,
Write the expression for distance covered between them during reaction time .
Here,
Write the expression for remaining distance between trainsafter reaction time
Here,
Write the expression for final relative velocity between the trains
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the minimum negative acceleration to avoid collision is
(b)
Velocity of passenger train at minimum acceleration to avoid collision
(b)
Answer to Problem 88P
Velocity of passenger train at minimum acceleration to avoid collision is
Explanation of Solution
Given:
Reaction time is
Formula used:
Write expression for distance remaining between trains after reaction time
Here,
Write expression for final relative velocity.
Here,
Write expression for final relative velocity.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the velocity of passenger train at minimum acceleration to avoid collision is
(c)
Distance covered by passenger train between sighting and collision
(c)
Answer to Problem 88P
The distance covered by passenger train between sighting and collision is
Explanation of Solution
Formula used:
Write the expression for time when train just collides.
Write the expression for distance covered by passenger train between sighting and collision
Here,
Calculation:
Substitute
Substitute
Conclusion:
Distance covered by passenger train between sighting and collision is
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