A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s2. its maximum cruising speed is 120 mi/h. (round yo
ur answers to three decimal places.) (a) 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?
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 = <span>120 mi/h (0.25h)</span> = 30 miles
