Question 1184685
A train moving at 12 m/s accelerates to 36 m/s over a distance of 8.0 km. 
(A) what is the train's acceleration? <pre>


Change 8.0 km to 8000 m so we don't mix km's with m's
{{{matrix(5,3,
v[F]^2-v[O]^2,""="",2as,
36^2-12^2,""="",2a(8000),
1296-144,""="",16000a,
1152,""="",16000a,
0.072,""="",a)}}}

An acceleration of 0.072 m/s².</pre>
(B) how much time does it take the train to reach 36 m/s?<pre> 

{{{matrix(5,3,

v[F]-v[O],""="",at,
36-12,""="",(0.072)t,
24,""="",0.072t,
(24)/(0.072),""="",t,
333.3,""="",t)}}}

333.3... seconds, divide by 60, 5.556 minutes</pre> 
(C) what is the average velocity of the train?<pre>
{{{matrix(4,3,

a[av],""="",(v[F]+v[O])/2,
a[av],""="",(36+12)/2,
a[av],""="",48/2,
a[av],""="",24
)}}}

average speed = 24 m/s

Edwin</pre>