Question

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?

Answer 1

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

Answer 2

(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