Ahigh-speed bullet train accelerates and decelerates at the rate of 10 ft/s2. its maximum cruising speed is 120 mi/h. (round your 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 = 120 mi/h (0.25h) = 30 miles

Maximum distance the train can travel,

D = d1 + d2 = 0.293 + 30  miles = 30.293 miles