Acceleration due to Gravity

Establishing a consistent coordinate system is the most critical step in solving vertical motion problems. You must define one direction (either upwards or downwards) as positive and apply this strictly to displacement, velocity, and acceleration.

If upwards is positive, then the acceleration $a = -g$ (since gravity pulls down), initial upward velocity $u$ is positive, and displacement $s$ is positive when the object is above the starting point.

If downwards is positive, then $a = g$, and any upward motion (like an initial throw) must be recorded as a negative velocity. This convention is often simpler for objects dropped from a height.

When an object is projected upwards, it experiences a continuous downward acceleration that reduces its upward velocity until it reaches its highest point.

At this instantaneous peak, the vertical velocity is exactly $v = 0$. This is a 'hidden' piece of information that allows you to solve for height or time using SUVAT equations.

Note that while the velocity is zero at the peak, the acceleration remains constant at $g$. The object does not 'stop' accelerating; it simply changes direction.

Displacement ($s$) is a vector quantity representing the change in position relative to the starting point. If an object is thrown up and caught at the same height, its total displacement is $s = 0$.

Distance is a scalar quantity representing the total path traveled. For an object thrown to a height $H$ and back, the total distance is $2H$, whereas the displacement is zero.

In SUVAT equations, the variable $s$ always refers to displacement. Using distance instead of displacement in these formulas will lead to incorrect results for time and velocity.

Significant Figures: When using $g = 9.8$, your final answer should generally be rounded to 2 or 3 significant figures. Providing more digits implies a level of precision that the input value of $g$ does not support.

Impact Velocity: A common misconception is that the final velocity $v$ is zero when an object hits the ground. In mechanics models, $v$ refers to the velocity the instant before impact; the impact itself is a separate event involving different forces.

Symmetry of Motion: For objects returning to their original launch height, the time taken to reach the peak is exactly half the total flight time, and the impact speed will equal the launch speed (in the absence of air resistance).