what
is the maximum distance the train can travel if it accelerates from
rest until it reaches its cruising speed and then runs at that speed for
15 minutes?
d = vo*t + 0.5*a*(t**2) ..........................(vo= initial speed = 0; a= acceleration; t=time, d = distance)
Vf = vo + a*t (final speed, in this case it will be the cruising speed)
Since vo = 0 (starts from rest)
t = Vf/a
d = 0 + 0.5*a*((Vf/a)**2)
d = (0.5/a)*(Vf)**2
a = 24545 miles/h2 = 10ft/s2
d1 = (0.5/24545 miles/h2)*(120 mi/h)**2 = 0.293 miles
From cruising speed, distance traveled after 15 minutes (0.25h)
v = d/t ...................> d2 =v*t = 120 mi/h (0.25h) = 30 miles
Maximum distance the train can travel,
D = d1 + d2 = 0.293 + 30 miles = 30.293 miles
