Can an object have zero velocity but non-zero acceleration at the same instant?

Assume the length of train be I and its acceleration be a.

$v^2=u^2+2al\Rightarrow al=\frac{v^2-u^2}{2}$

Velocity when middle point crosses the post,

$V_m=\sqrt[]{u^2+2a\frac{\mathcal{l}}{2}}.=\sqrt[]{u^2+\frac{v^2-u^2}{2}}=\sqrt[]{\frac{u^2+v^2}{2}}$

Sign conventions are important because all kinematic variables can be positive or negative. You must first choose your coordinate system and positive direction, then consistently apply signs. For example, if you are choosing upward as positive in free-fall problems, gravity becomes negative (a = -g), upward initial velocity is positive, and downward displacement is negative. The equations of motion work for any situation, as long as you substitute values with proper signs. Incorrect conventions lead to wrong answers.

It's not always true. Direction of velocity is the most important consideration here that will tell us whether acceleration increases or decreases speed. You can consider two scenarios. If you're falling, that's negative velocity. That implies negative gravitational acceleration. Here, your speed increases. If you're moving upward, that's positive velocity. Now, with that same negative acceleration, your speed decreases. For choosing the equations of motion, you need to know both the signs of acceleration and velocity to determine if you're speeding up or slowing down.