$a_{\text{avg}}=\dfrac{\Delta v}{\Delta t}$

$a_{\text{avg}}$ = average acceleration in $\text{m/s}^2$

$</p><p>\Delta v=v_f-v_i$</p><p>$\Delta v$= change in velocity in$\text{m/s}$</p><p>$$</p><p>$\Delta t=t_f-t_i$</p><p>$\Delta t$= time interval in$\text{s}$</p><p>$$</p><p>$v_f$</p><p>$v_f$= final velocity at the end of the interval in$\text{m/s}$</p><p>$$</p><p>$v_i$</p><p>$v_i$= initial velocity at the start of the interval in$\text{m/s}$</p></div><p>Use consistent units (typically <strong>meters</strong>, <strong>seconds</strong>) and keep track of the signs of velocities.</p><h2 class="editor-heading" id="direction-signs-and-interpretation-1-d"><strong>Direction, Signs, and Interpretation (1D)</strong></h2><h3 class="editor-heading"><strong>Choosing a positive direction</strong></h3><p>In one dimension, direction is handled by a <strong>sign convention</strong>:</p><ul><li><p>Pick a positive direction (for example, rightward or upward).</p></li><li><p>Velocities in the positive direction are <strong>positive</strong>; in the opposite direction are <strong>negative</strong>.</p></li><li><p>Average acceleration inherits its sign from$\Delta v$(since$\Delta t$is positive if time moves forward).</p></li></ul><h3 class="editor-heading"><strong>What the sign tells you</strong></h3><p>The sign of$a_{\text{avg}}$tells you the direction of the velocity change:</p><ul><li><p>$a_{\text{avg}} > 0$: velocity becomes more positive (could mean speeding up in + direction or slowing down in − direction).</p></li><li><p>$a_{\text{avg}} < 0$: velocity becomes more negative (could mean slowing down in + direction or speeding up in − direction).</p></li><li><p>$a_{\text{avg}} = 0$: no net change in velocity over the interval (velocity could be constant).</p></li></ul><p>Avoid the common mistake of assuming “negative acceleration” automatically means “slowing down.”</p><img src="https://tutorchase-production.s3.eu-west-2.amazonaws.com/e9ea75da-d068-446e-9ccd-b53414e984e6-file.png" alt="Pasted image" style="width: 820px; height: 301px; cursor: pointer;" width="820" height="301" draggable="true"><p><em>A set of representative$v$–$t$graphs showing that speeding up corresponds to the velocity moving away from zero, while slowing down corresponds to the velocity moving toward zero. The four cases clarify that the sign of acceleration depends on the slope of$v(t)$, not on whether the object is “slowing down” in everyday language. </em><a target="_blank" rel="noopener noreferrer nofollow" href="https://www.physicsclassroom.com/getattachment/Physics-Video-Tutorial/Kinematics/Velocity-Time-Graphs-Changing-Speed/Lecture-Notes/VelocityTimeGraphs2.pdf?lang=en-US"><em>Source</em></a></p><p>Slowing down happens when <strong>velocity and acceleration have opposite signs</strong>.</p><h2 class="editor-heading" id="selecting-the-interval-and-reading-information"><strong>Selecting the Interval and Reading Information</strong></h2><h3 class="editor-heading"><strong>The interval matters</strong></h3><p>Average acceleration depends on the chosen start and end times:</p><ul><li><p>Over a longer interval,$a_{\text{avg}}$reflects the overall change.</p></li><li><p>Over a shorter interval, it can be different if the motion varies.</p></li></ul><p>To compute it correctly, you must identify:</p><ul><li><p>The <strong>initial velocity</strong> at the start of the interval</p></li><li><p>The <strong>final velocity</strong> at the end of the interval</p></li><li><p>The <strong>time interval</strong> between those two moments</p></li></ul><h3 class="editor-heading"><strong>Practical notes for AP problems</strong></h3><p>When velocities are given with directions (or signs), treat them as <strong>signed values</strong>:</p><ul><li><p>“$3\ \text{m/s}$east” and “$-3\ \text{m/s}$” can represent the same velocity if east is defined as positive.</p></li><li><p>If an object reverses direction during the interval,$v_i$and$v_f$may have opposite signs, making$\Delta v$large in magnitude.</p></li></ul><p>Units check:</p><ul><li><p>Velocity:$\text{m/s}$</p></li><li><p>Time:$\text{s}$</p></li><li><p>Acceleration:$\text{m/s}^2$(read as “meters per second per second”)</p></li></ul><h2 class="editor-heading" id="common-errors-to-avoid"><strong>Common Errors to Avoid</strong></h2><ul><li><p>Using speed instead of velocity (speed has no sign; average acceleration needs <strong>velocity</strong>).</p></li><li><p>Mixing directions without a consistent sign convention.</p></li><li><p>Forgetting that$\Delta v = v_f - v_i$ (order matters).