At an amusement park, an engineer proposes a new at accelerate a string of train

Question

At an amusement park, an engineer proposes a new at accelerate a string of train cars from rest up to a speed of 30 mi/hr. The accelerator can generate a constant 60 hp and deliver 92% of that power to the train in tractive force. Starting from rest, what distance will the 2800 lb car have traveled when it reaches 30 mi/hr? [Hint: The car does not accelerate at a constant rate. Starting with governing equations and definitions, integrate to develop an equation for distance as a function of mass, power, and velocity.J

Explanation / Answer

P = 60 hp = 60 x 745.7 = 44742 Watt  

P_effective = 0.92 P = 41659.44 W

v = 30 x 1609 m / 3600 s = 13.41 m/s

m = 2800 lb = 1271.2 kg

Q = m v^2 /2 = 114298.74 J

Q = P t

t = Q/p_effective = 2.74 sec  

vf = vi + a t

13.41 = 0 + 2.74 a

a= 4.9 m/s^2

d = vi t + a t^2 /2 = 0 + (4.9)(2.74^2)/2

d = 18.4 m

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