Motion along a straight line

Rest and motion, defined against something. An object is in motion if its position changes with time relative to a chosen point. It is at rest if its position stays fixed relative to that same point. Neither word means anything on its own — you must always finish the sentence "at rest with respect to..." or "in motion with respect to...". This reference point, together with a set of coordinate axes used to measure position from it, is called a frame of reference.

Why "relative" is not a throwaway word. A passenger seated in a moving train is at rest with respect to the train and to the person beside him — his seat, his tray table, his position inside the compartment never change. The same passenger is in motion with respect to a tree outside or a person standing on the platform, because his distance from that tree keeps growing. Nothing about the passenger himself has changed between these two descriptions; only the frame of reference used to judge him has. There is no frame-free, "absolute" answer to "is he moving?" — physics simply does not ask that question in isolation.

Straight-line (rectilinear) motion. The special case this chapter starts with is motion confined to a single straight line — also called rectilinear or one-dimensional motion. A car on a straight road, a stone falling vertically, or a train on a straight track are everyday examples. Because the path is a line, the position of the object at any instant needs only one number: its distance from a fixed starting point, together with which side of that point it lies on (for example, "3 m to the right" or "-3 m," using a sign convention). This is simpler than motion on a curved path or in a plane, where two or three numbers would be needed, which is exactly why NCERT introduces straight-line motion first.

A word of caution. "Rectilinear" only describes the shape of the path — a straight line. It says nothing about speed. A car speeding up, slowing down, or briefly stopping at a signal, while staying on the same straight road, is still undergoing rectilinear motion throughout.

Motion is always about change of position, and "position" itself is meaningless until you pick a reference point to measure it from. Two different reference points can give two different, equally correct answers about the same object at the same moment — this is not a flaw in physics, it is the whole point. Take the passenger again. Measured from the train's frame — its walls, seats and floor — his coordinates never change, so he is at rest. Measured from the ground's frame — the platform, the tree, the fixed points along the track — his distance from those fixed points keeps increasing as the train moves, so he is in motion. Both statements describe the exact same physical situation; neither is "more true" than the other. What changes between them is only the ruler being used, not the passenger. This idea scales all the way up. A table, chair and clock fixed inside a room are at rest with respect to the room's walls and floor — the frame we use without thinking about it in everyday life. But the room sits on the Earth, which spins on its axis and orbits the Sun. Judged against the Sun as a reference point, the table, chair, clock and the entire house are sweeping through space at enormous speed. So even objects that "obviously never move" are only at rest within one particular, unstated frame — which is why physicists insist on naming the frame explicitly, a habit that pays off later once distance, speed and velocity become measured numbers that a wrongly assumed frame would get wrong. Straight-line motion inherits this same logic but keeps the bookkeeping simple: once a frame of reference and a starting point on the line are fixed, one signed number is all that is needed to say exactly where the object is at a given instant, and how that single number changes with time tells the whole story of the motion.

A boy is sitting inside a bus moving at a steady pace on a straight highway. His friend stands at a bus stop, watching the bus go past. A bird happens to be flying alongside the bus, exactly matching its speed. Decide whether the boy is at rest or in motion in each of these three frames of reference: (a) the bus, (b) the ground where the friend stands, and (c) the flying bird.

Step 1. Frame = the bus. The boy's position inside the bus — which seat, how far from the door — does not change as the journey continues. Relative to the bus, the boy is at rest.

Step 2. Frame = the ground (the friend's frame). As the bus moves down the highway, the boy's distance from the friend and from any fixed point on the ground keeps increasing. Relative to the ground, the boy is in motion.

Step 3. Frame = the bird. The bird is flying alongside the bus at exactly the bus's speed, so the distance between the bird and the boy is not changing either. Relative to the bird, the boy is also at rest — just as he was relative to the bus, even though bird and bus are two completely different objects.

Answer: the boy is at rest with respect to the bus and the bird, and in motion with respect to the ground/his friend, all at the same instant. No answer here is wrong; each is correct once its frame is stated, and the same object can be "at rest" in more than one frame if those frames move together.

Competitive stretch

If a second bird flies alongside the bus but in the opposite direction to the bus's motion, is the boy at rest or in motion relative to that bird? Since the bird's position relative to the ground is changing differently from the boy's, their separation keeps changing too — so the boy is in motion relative to this second bird, even though both birds are "flying alongside" in some loose everyday sense. The lesson: rest and motion depend on whether the separation between the two objects changes, not on how the situation is described in words.

• Treating "at rest" or "in motion" as true in some absolute sense, without naming a frame of reference — the question "is it moving?" is incomplete on its own.
• Assuming the ground is automatically a fixed, "true" frame because it feels stationary underfoot — the ground itself is moving along with the spinning, orbiting Earth relative to the Sun.
• Mixing up "frame of reference" with just the coordinate axes — the frame includes both the reference point and the axes used to measure position from it.
• Believing rectilinear motion means constant speed or no stopping — it only means the path traced out is a straight line; speed along that line can still increase, decrease, or momentarily reach zero.

Ask the tutor: curious how a satellite can look "fixed" over one spot on Earth, or why we don't feel the Earth spinning beneath us — ask the AI tutor to walk through more everyday examples of relative motion and frames of reference.