Motion, Distance, Displacement and Speed
Motion, Distance, Displacement and Speed
The science half of Part-III carries about 40 questions, and physics takes roughly a third of them. Motion is the opening chapter of that block and gives 2 questions. It is examined through definitions and graph reading rather than heavy calculation, so precision matters more than speed here.
Distance and Displacement
| Point | Distance | Displacement |
|---|---|---|
| Meaning | Total path covered | Shortest gap from start to end |
| Direction | Not considered | Considered |
| Quantity type | Scalar | Vector |
| Can it be zero | Only if no movement | Yes, on returning to start |
| Comparison | Always greater or equal | Always less or equal |
A runner completing one lap of a 400 metre track covers a distance of 400 metres and a displacement of zero. That example is used in the class 9 textbook and is asked almost verbatim.
✗ Displacement can be greater than distance | ✓ Displacement is never greater than distance; at most they are equal
Speed, Velocity and Acceleration
Speed = distance ÷ time | Velocity = displacement ÷ time
Acceleration = (final velocity − initial velocity) ÷ time
- Speed is scalar; velocity is a vector with direction.
- Uniform motion means equal distances in equal intervals of time.
- Acceleration is negative when the body slows down, which is called retardation.
- A body moving in a circle at constant speed is still accelerating, because its direction keeps changing.
That last point is the standard reasoning question, because it separates constant speed from constant velocity.
The SI unit of speed and velocity is metre per second, and of acceleration is metre per second squared. To convert km/h to m/s, multiply by 5/18.
The Equations of Motion
v = u + at | s = ut + ½at² | v² = u² + 2as
These apply only to uniformly accelerated motion in a straight line. For a body starting from rest, u is zero, which simplifies all three. For a body under gravity, a is replaced by g, about 9.8 metre per second squared, taken as positive downwards.
Graphs of Motion
| Graph | What the slope means | Shape for uniform motion |
|---|---|---|
| Distance-time | Speed | Straight sloping line |
| Velocity-time | Acceleration | Horizontal line |
| Distance-time (at rest) | Zero speed | Horizontal line |
| Velocity-time (uniform acceleration) | Constant acceleration | Straight sloping line |
On a velocity-time graph, the area under the curve gives the distance travelled. That single fact answers a whole family of questions and is often the only way to solve them quickly.
चाल अदिश राशि है, वेग सदिश — वेग में दिशा भी शामिल है।
TRE pointer: Part-III science is worth about 40 questions against roughly 8 in Part-II, so physics here is examined at NCERT class 8 and 9 depth rather than as general knowledge. The two items that repeat are the circular motion at constant speed reasoning question and the area-under-a-velocity-time-graph result. Since you will teach graph reading yourself, expect a graph-based question rather than a plain numerical. With five options and −1/3 for a wrong answer, read the axis labels before the options.
60-Second Recap
- Distance is scalar and total path; displacement is vector and shortest gap.
- Displacement is never greater than distance and can be zero.
- Speed uses distance, velocity uses displacement; km/h to m/s is × 5/18.
- Circular motion at constant speed is still accelerated, because direction changes.
- The three equations of motion apply only to uniform acceleration in a straight line.
- Slope of a distance-time graph is speed; area under a velocity-time graph is distance.
Frequently Asked Questions
Can displacement be zero while distance is not?
Yes. If a body returns to its starting point, the shortest gap between start and finish is zero, so displacement is zero, while the path actually covered may be large. A runner completing one lap of a track is the standard example used in textbooks.
Is a body moving in a circle at constant speed accelerating?
Yes. Acceleration means any change in velocity, and velocity includes direction. In circular motion the direction changes continuously even though the speed does not, so the body is accelerating. This distinction between speed and velocity is asked as a reasoning question.
What does the area under a velocity-time graph represent?
The distance travelled during that interval. The slope of the same graph gives the acceleration. For a distance-time graph, by contrast, the slope gives the speed and the area has no useful physical meaning. Mixing up the two graphs is a frequent error.
When can I use the three equations of motion?
Only when the acceleration is uniform and the motion is along a straight line. They do not apply to circular motion or to motion where the acceleration changes. For a body starting from rest the initial velocity is zero, which simplifies all three equations.