Uniformly Accelerated Motion (UAM)
Overview
Constant acceleration means the velocity changes by the same amount each second. The x–t graph is a parabola (curved). The v–t graph is a straight line (slope = acceleration). The four SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Any three known quantities let you find the other two.
What is uniformly accelerated motion?
Uniformly accelerated motion (eenparig versnelde beweging) occurs when acceleration is constant. The velocity changes by the same amount every second. The x–t graph is a parabola (the object covers more and more distance each second). The v–t graph is a straight line; its slope equals the acceleration. The a–t graph is a horizontal line at the value of a.
The four SUVAT equations
These four equations link the five kinematic variables: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time). Each equation uses four of the five variables. Step 1: identify which three variables are given. Step 2: choose the equation that contains only those three and the unknown. The equations are: (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as, (4) s = ½(u+v)t.
Sign conventions — critical for every problem
Always define a positive direction before solving. Typically 'up is positive' or 'right is positive'. If an object moves against your positive direction, its velocity is negative. Gravity acts downward, so if up is positive, a = −9.81 m/s². If you define downward as positive, then a = +9.81 m/s². Be consistent throughout the entire problem — never switch mid-calculation.
- ⚠Using the wrong equation — list your known/unknown variables first before choosing
- ⚠Forgetting that at the top of a trajectory, v = 0 but a ≠ 0
- ⚠Not defining a sign convention — causes errors with negative values of s or v
- ⚠Using g = 10 m/s² when the question says to use 9.81 m/s²
- ⚠Forgetting that the area under a v–t graph gives displacement, not distance (displacement can be negative)