A light-rail commuter train draws train draws 635 A of 650-V DC electricity when

Question

A light-rail commuter train draws train draws 635 A of 650-V DC electricity when accelerating. What is its power consumption rate in kilowatts? Numeric: A numeric value is expected and not an expression. P = ________ How many seconds does it take to reach 21.5 m/s starting from rest if its loaded mass is 5.15 middot 10^4 kg, assuming 95.0% efficiency and constant power? Numeric A numeric value is expected and not an expression. t = ___________ Find its average acceleration, in meters per square second. Numeric: A numeric value is expected and not an expression. a = _________

Explanation / Answer

Given I = 635 A

voltage V = 650 V

part a)

power consumption P = V * I

P = 650 * 635

P = 412.75 kW

part b)

velocity v = 21.5 m/s

mass m = 5.15 * 10^4 kg

work W = K.E = 1/2 * m * v^2

W = 1/2 * 5.15 * 10^4 * (21.5)^2

W = 1.19 * 10^7 J

power P = W / t

412750 = 1.19 * 10^7 / t

t = 28.83 s

part c)

from v = u + a*t

21.5 = 0 + (a * 28.83)

acceleration a = 0.745 m/s^2

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