Question

A train is traveling at 55m/s begins to slow down as it approaches a bend in the tracks. If it travels around the bend at a speed of9 m/s and it takes 49 s to properly slow down, what distance does the train travel while slowing down?

Answer 1

x = 1127 [m]

Step-by-step explanation:

In order to solve this problem, we must use the equations of kinematics. With the first equation, we must find the acceleration and with the second equation we must find the distance.

`v_(f) =v_(o) -a*t`

where:

Vf = final velocity = 9 [m/s]

Vo = initial velocity = 55 [m/s]

a = acceleration o desacceleration [m/s²]

t = time = 49 [s]

Now replacing:

9 = 55 - a*49

a*49 = 55 + 9

a = 1.306 [m/s²]

Note: The negative sign in the above equation means that the speed decreases.

Now using the second equation.

`v_(f)^(2) =v_(o)^(2) -2*a*x`

(9)² = (55)² - 2*(1.306)*x

2944 = 2.612*x

x = 1127 [m]