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Class 9 Describing Motion Around Us: cheat sheet
CBSE Science. Distance, displacement, speed, velocity and acceleration, the three equations of motion, and reading distance–time and velocity–time graphs.
Key ideas
- Distance is the total path; displacement is the straight-line change in position, with a direction.
- Speed has no direction; velocity has one. Average speed = total distance ÷ total time.
- Acceleration is the rate of change of velocity; it is negative (retardation) when an object slows down.
- The slope of a distance–time graph gives speed; the slope of a velocity–time graph gives acceleration.
- The area under a velocity–time graph gives the displacement.
- Uniform circular motion has constant speed but changing direction, so it is accelerated.
Remember
| Acceleration | a = (v − u) ÷ t |
| Equations of motion | v = u + at; s = ut + ½at²; v² − u² = 2as |
| Circular motion | v = 2πr ÷ t |
| Units | km/h × 5/18 = m/s |
Watch out
- Using km/h in an equation with m and s: convert first.
- Taking u as 0 when the object does not start from rest.
- Giving a distance when a displacement is asked (one full round has displacement 0).
Worked example
An athlete completes one round of a circular track of radius 28 m in 30 s. What distance has the athlete covered, and what is the displacement, after 135 s? (π = 22/7)
Working: 135 s = 4 ½ rounds; distance = 4 ½ × 2πr; displacement = diameter = 56 m
Answer: distance 792 m; displacement 56 m
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