What is the final speed of a bullet train accelerating at a rate of 200 kilometer per hour squared from an initial speed of 150 kilometer per hour over a distance of 100 km.?

Answer 1

Here's a good old reliable formula that typically shows up with time in seconds,

but if we're careful and keep everything consistent, there's no reason that it

shouldn't work just as well for this situation, with the time in hours:

Distance = s0 T + 1/2 A T2

Distance = 100 km

s0 = initial speed = 150 km/hr

A = acceleration = 200 km/hr2

Let's see what that does for us:

100 = 150 T + 100 T2

T2 + 1.5 T - 1 = 0

T = 1/2 [ -1.5 ± sqrt(2.25 + 4) ] = 1/2 [ -1.5 ± sqrt(6.25) ]

T = 1/2 hr

T = -2 hr

The solution T=-2 hr is technically perfect, mathematically impeccable,

and realistically useless. We'll use the solution T=0.5 hour .

-- T = 0.5 hour when the train has covered 100 km.

-- In 1/2 hour, its speed has increased by 1/2 of the acceleration value = 100 km/hr.

-- With its muzzle velocity of 150 km/hr, the bullet train's speed after the 1/2 hour is 250 km/hr .