Velocity at an intermediate point of a uniformly accelerating body

A body undergoes constant acceleration over a known distance, and the question asks for the velocity at a specific intermediate point (e.g., midpoint) given initial and final velocities.

ap-calculus-ab None Q12 View
12. A particle travels in a straight line with a constant acceleration of 3 meters per second per second. If the velocity of the particle is 10 meters per second at time 2 seconds, how far does the particle travel during the time interval when its velocity increases from 4 meters per second to 10 meters per second?
(A) 20 m
(B) 14 m
(C) 7 m
(D) 6 m
(E) 3 m
jee-main 2012 Q2 View
A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard's room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.
(1) $\frac { u + v } { 2 }$
(2) $\frac { 1 } { 2 } \sqrt { u ^ { 2 } + v ^ { 2 } }$
(3) $\sqrt { u v }$
(4) $\sqrt { \left( \frac { u ^ { 2 } + v ^ { 2 } } { 2 } \right) }$