Kinematic Equation Uniformly of Accelerated Motion

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Vishal Baghel

Contributor-Level 10

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

v 2 = u 2 + 2 a l a l = v 2 u 2 2

Velocity when middle point crosses the post,

V m = u 2 + 2 a l 2 . = u 2 + v 2 u 2 2 = u 2 + v 2 2

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Syed Aquib Ur Rahman

Contributor-Level 10

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.

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New answer posted

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Syed Aquib Ur Rahman

Contributor-Level 10

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.

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Syed Aquib Ur Rahman

Contributor-Level 10

Zero velocity doesn't mean zero acceleration. When you throw a ball-like object upward, at its peak the velocity is zero. But acceleration remains constant due to gravity. The velocity is still changing from positive to negative at that instant. That means acceleration continues.

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