Light-rail passenger trains that provide transportation within and between cities are capable of modest accelerations. The magnitude of the maximum acceleration is typically 1.3 m/s2, but the driver will usually maintain a constant acceleration that is less than the maximum. A train travels through a congested part of town at 4.0m/s. Once free of this area, it speeds up to 13m/s in 8.0 s. At the edge of town, the driver again accelerates, with the same acceleration, for another 16 s to reach a higher cruising speed.

What is the final speed?

Express your answer to two significant figures and include the appropriate units.

Question

Dorian Vaughan

Physics

23 October, 21:50

Light-rail passenger trains that provide transportation within and between cities are capable of modest accelerations. The magnitude of the maximum acceleration is typically 1.3 m/s2, but the driver will usually maintain a constant acceleration that is less than the maximum. A train travels through a congested part of town at 4.0m/s. Once free of this area, it speeds up to 13m/s in 8.0 s. At the edge of town, the driver again accelerates, with the same acceleration, for another 16 s to reach a higher cruising speed.

What is the final speed?

Express your answer to two significant figures and include the appropriate units.

+4

Answers (1)

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Nikolas Gallagher · Answer 1

During the first phase of acceleration we have:

v o = 4 m/s; t = 8 s; v = 13 m/s, a = ?

v = v o + a * t

13 m/s = 4 m / s + a * 8 s

a * 8 s = 9 m/s

a = 9 m/s : 8 s

a = 1.125 m/s²

The final speed:

v = ?; v o = 13 m/s; a = 1.125 m/s²; t = 16 s

v = v o + a * t

v = 13 m/s + 1.125 m/s² * 16 s

v = 13 m/s + 18 m/s = 31 m/s