Freight trains can produce only relatively small acceleration and decelerations. (a) what is the final velocity (in m/s) of a freight train that accelerates at a rate of 0.0600 m/s2 for 8.00 min, starting with an initial velocity of 5.00 m/s?

For this problem, we use the derived equations for rectilinear motion at constant acceleration.

a = (v - v₀) / t

where

a is acceleration

v₀ and v are the initial and final velocities, respectively

x is the distance

t is the time

The solution is as follows:

a = (v - v₀) / t

0.06 m/s² = (v - 5 m/s) / (8 min * 60 s/1 min)

Solving for v,

v = 33.8 m/s

(a) We will use the equation v = u + at

Initial velocity u = 5.00 m/s

Acceleration a = 0.0600 m/s²

time = 8 min = 8 x 60 = 480 s

Final velocity

= u + at

= 5.00 + 0.0600 (480)

= 33.8 m/s

The final velocity is 33.8 m/s