What do such kilometre stones indicate? How could Padma conclude that she was getting closer to her destination?
Answer
A kilometre stone shows the distance of that spot from a named place — here, from Delhi. Delhi is the reference point, and the number on the stone is Padma's position with respect to it.
Positions of kilometre stones with respect to Delhi as a reference point (as in Fig. 5.13).
How Padma could tell she was getting closer: she compared two readings taken at two different times.
Earlier stone: position = 70 km from Delhi
Later stone: position = 60 km from Delhi
Distance covered between the two stones = 70 km − 60 km = 10 km
The number is getting smaller ⇒ the bus is moving towards Delhi.
Had the numbers been rising — 60 km, 70 km, 80 km — she would have known the bus was moving away from Delhi.
Why it happens: a kilometre stone does not measure how far the bus has travelled from home. It measures the gap between the bus and the reference point. When that gap shrinks with time, the bus is approaching; when it grows, the bus is receding.
Did you know? The colour of the top of an Indian milestone tells you the kind of road — yellow for a National Highway, green for a State Highway, black or blue for a district or city road, and orange for a village road built under Pradhan Mantri Gram Sadak Yojana.
Q2.
Does this mean that the position of Padma, with respect to the reference point, is changing with time? When does the position of an object change with respect to a reference point? Does it change when an object is moving?
Answer
Yes to all three. Take them one at a time.
(i) Is Padma's position changing with time? Yes. At one moment she was 70 km from Delhi; a little later she was 60 km from Delhi. The reference point (Delhi) did not move, the road did not move — only Padma did. So her position with respect to Delhi is changing as time passes.
(ii) When does the position of an object change with respect to a reference point? Only when the gap between the object and that point changes. That happens when the object moves nearer or farther, and it is measured by comparing readings at two different times.
Position at time 1 = 70 km from Delhi
Position at time 2 = 60 km from Delhi
Change of position = 10 km, towards Delhi
(iii) Does it change when an object is moving? Yes — and this is exactly how motion is defined in the very next section:
An object is said to be in motion if its position changes with respect to the reference point with time.
If the position does not change with time, the object is said to be at rest.
One careful point: the object must move relative to the chosen reference point. If Padma's bag is on the seat beside her, it is at rest with respect to Padma even though both are speeding along the highway — because the gap between Padma and her bag never changes. Motion and rest always depend on which reference point you pick.
Tip: Two readings are always needed to decide motion — one position is never enough. “70 km from Delhi” alone tells you where she is, not whether she is moving.