u/visheshnigam

High-impact mind maps for mastering reference frames. Includes the vector addition rule, the flip rule (v_ᴀ/ʙ = -v_ʙ/ᴀ), and the distinction between inertial and non-inertial systems.

You're driving at 100 km/h. A truck overtakes you at 120 km/h. From your frame, the truck moves forward at 20 km/h — that makes sense. But from the truck driver's frame, you appear to be moving backward at 20 km/h. Neither driver is wrong.
This is relative velocity in action. Velocity is not a fixed property of an object — it is always a measurement between an object and a specific observer's reference frame. Change the observer, change the number. The physics doesn't change. The description does.

Quick and critical: the area under a v-t graph gives displacement, not distance, and definitely not position. Three things students mess up constantly.

First — the units are meters, not meters squared. Multiply the axis labels: (m/s) × s = m. Second — area below the time axis is negative because velocity is negative, meaning the object moves backward. On FRQs, saying “it’s below the axis” is not enough — you must state the direction of motion. Third — area gives the change in position. To find where the object is, you need x₁ = x₀ + area.

Same logic works for a-t graphs: area = change in velocity.