A reference frame is the coordinate system an observer uses to measure position, velocity, and time. It includes a chosen origin, a positive direction, and a clock. Every measurement of motion is made relative to some frame— there is no such thing as "true" motion measured from nowhere.
When you say a car moves at 30 m/s, you almost always mean "relative to the road." But the road frame is just one choice. A passenger in another car, a pilot overhead, or a person on a train all carry their own frames, and each is equally valid.
Imagine you are walking forward at 1 m/s down the aisle of a train that is moving at 20 m/s along the tracks. How fast are you going? It depends entirely on who's asking.
You move at 1 m/s — just your walking speed down the aisle.
You move at 21 m/s — your walking plus the train's motion.
Both answers are correct. They describe the same walking, measured from two different frames. Neither observer is "wrong" — they simply chose different origins that move relative to one another.
To find the velocity of an object as seen by a moving observer, subtract the observer's velocity from the object's velocity. Both must be measured in the same (usually ground) frame first.
Use the explorer below. Both arrows on top are measured from the ground; the bottom green arrow is what the moving observer actually sees. Notice how when the observer matches the object's velocity, the object appears to stop.
Both velocities are measured from the ground. The bottom arrow shows the object as seen by the moving observer— that's the relative velocity v₍rel₎ = v₍obj₎ − v₍obs₎.
Relative velocity problems in AP Physics 1 live on a single axis, so the only tricky part is bookkeeping the signs. Pick a positive direction first and stick with it for every velocity in the problem.
Car A drives east at 25 m/s. Car B drives west at 15 m/s. How fast does Car A approach Car B — that is, what is Car A's velocity in Car B's frame?
An inertial reference frameis one that is not accelerating — it moves at constant velocity (including the special case of being at rest). In an inertial frame, Newton's laws hold in their simplest form, with no mysterious extra forces.
A train rolling at a steady 20 m/s is an inertial frame: a ball set on the floor stays put. But the moment the train brakes, that frame is accelerating, and the ball seems to roll forward on its own. For AP Physics 1, we assume frames are inertial unless told otherwise.
Here is the surprising payoff: although velocity changes from frame to frame, acceleration does not. As long as two frames move at constant velocity relative to each other, every observer measures the same acceleration for an object.
The reason is simple. The two frames differ by a constant velocity. When you compute acceleration as the rate of change of velocity, that constant difference is subtracted away — its rate of change is zero.
Set the object's velocity and the observer's velocity. Watch how the relative velocity changes.
Object moves faster than observer in the same direction — appears slower but still forward.
A ball speeds up from 4 m/s to 10 m/s in 2 s, measured from the ground. A train moving at a constant 5 m/s passes by. Show the train observer measures the same acceleration.