The Problem:
A train travelling at 55 m s1 has to reduce speed to 35 ms to pass through a junction. If the deceleration is not to exceed 0.6 m s2, how far ahead of the junction should the train begin to slow down?
Douglas Quadling Mechanics1 Exercise1C Q5
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Problem Statement:
A train traveling at 55 m/s has to reduce its speed to 35 m/s to pass through a junction. If the deceleration is not to exceed 0.6 m/s², how far ahead of the junction should the train begin to slow down?
Solution:
Step 1: Write Down the Equation of Motion
The equation of motion is:
Final Velocity² = Initial Velocity² + 2 * Acceleration * Distance
Step 2: Substitute the Known Values
Substitute Initial Velocity (u) = 55 m/s, Final Velocity (v) = 35 m/s, and Acceleration (a) = -0.6 m/s²:
35² = 55² + 2 * (-0.6) * s
Step 3: Simplify the Equation
Calculate the squares and substitute:
1225 = 3025 – 1.2 * s
Step 4: Solve for Distance (s)
Rearrange the equation to solve for s:
1225 – 3025 = -1.2 * s
-1800 = -1.2 * s
s = -1800 / -1.2 = 1500 metres
Final Answer:
The train should begin to slow down 1500 metres ahead of the junction.
Verification:
To ensure the answer is correct, let’s verify the calculations.
1. Substitute s = 1500 metres into the equation of motion:
Final Velocity² = Initial Velocity² + 2 * Acceleration * Distance
35² = 55² + 2 * (-0.6) * 1500
1225 = 3025 – 1800
1225 = 1225
2. The final velocity matches the required speed of 35 m/s, confirming that the distance s = 1500 metres is correct.
Conclusion:
The train should begin to slow down 1500 metres ahead of the junction to reduce its speed from 55 m/s to 35 m/s with a deceleration not exceeding 0.6 m/s².
