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Class 9 Understanding Motion through Experience (Advanced): cheat sheet
CBSE Science. Motion depends on the observer: frames of reference, relative speed, scalars and vectors, adding displacements, and the distance covered in one particular second.
Key ideas
- Rest and motion are always relative to a reference point; an inertial frame is at rest or moves at constant velocity.
- Two bodies moving the same way see each other at the difference of their speeds; moving towards each other, at the sum.
- Scalars (distance, speed, mass, time) have magnitude only; vectors (displacement, velocity, force) also have direction.
- Vectors add head to tail: the resultant joins the first tail to the last head; walks at right angles combine by Pythagoras.
- Distance is never less than the size of the displacement, which is zero for a round trip.
- From rest, the distances in successive seconds are in the ratio 1 : 3 : 5 : 7 …
Remember
| Equations of motion | v = u + at; s = ut + ½at²; v² = u² + 2as |
| Distance in the nth second | sₙ = u + a(2n − 1)/2 |
| Right-angled displacements | resultant = √(a² + b²) |
| Stopping distance | s = u² ÷ 2a, so doubling the speed makes it four times as long |
Watch out
- Using ut + ½at² (the total in n seconds) when the question asks for the nth second alone.
- Adding the speeds of two trains moving the same way.
- Adding perpendicular displacements as plain numbers instead of by Pythagoras.
Worked example
A toy car is pushed along a floor and its distance from the start O is marked every second: 2 m at 1 s, 6 m at 2 s, 12 m at 3 s, 20 m at 4 s. It moves with uniform acceleration. Find (a) the distance covered in the 3rd second, (b) the acceleration, (c) the initial velocity and (d) the velocity at 4 s.
Working: (a) 12 − 6; (b) each second's distance grows by a = 2; (c) s₁ = u + a/2 = 2; (d) v = u + 4a
Answer: (a) 6 m; (b) 2 m/s²; (c) 1 m/s; (d) 9 m/s
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