What are the three equations of motion for class 9?

For uniform acceleration: (1) v = u + at, (2) s = ut + ½at², and (3) v² = u² + 2as, where u is initial velocity, v final velocity, a acceleration, t time and s displacement.

What is the difference between distance and displacement?

Distance is the total path length covered (a scalar, always positive). Displacement is the shortest straight-line distance from start to finish with direction (a vector, can be zero or negative).

How do you find acceleration from a velocity-time graph?

Acceleration equals the slope of the velocity–time graph: a = (change in velocity) ÷ (time taken). The area under the velocity–time graph gives the displacement.

What is uniform and non-uniform motion?

In uniform motion an object covers equal distances in equal intervals of time (constant velocity, zero acceleration). In non-uniform motion the velocity changes, so the object has acceleration.

Class 9 · CBSE / NCERT · Science (Physics)

Motion — Class 9

The chapter that's all about numericals. Use the live grapher to feel how velocity and distance change, then let the solver walk you through every problem — the exact way you'd write it in the exam.

Distance vs DisplacementDistance = total path (scalar). Displacement = shortest path with direction (vector). On a round trip, displacement = 0 but distance ≠ 0.

Speed vs VelocitySpeed = distance/time (scalar). Velocity = displacement/time (vector). Unit: m/s.

Accelerationa = (v − u)/t. Unit: m/s². Negative acceleration (retardation) means slowing down.

Uniform motionEqual distances in equal times → constant velocity → zero acceleration → straight distance–time graph.

1. Motion Grapher Interactive

Set the initial velocity, acceleration and time. Watch the equations v = u + at and s = ut + ½at² draw themselves as velocity–time and distance–time graphs.

Initial velocity, u 5 m/s Acceleration, a 2 m/s² Time, t 6 s

Final velocity17 m/sv = 5 + 2×6

Displacement66 ms = 5×6 + ½×2×6²

Velocity–time

Slope = acceleration; area under it = displacement.

Distance–time

A curve (parabola) because distance grows with t².

2. Numericals Practice Interactive

A fresh problem every time. Work it out on paper, then reveal the full step-by-step solution and check your method.

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Which equation do I use? Pick the one missing the quantity you don't have: no displacement → v = u + at; no final velocity → s = ut + ½at²; no time → v² = u² + 2as.

3. Classic board numericals — solved

Q1. A car starting from rest accelerates uniformly at 4 m/s² for 5 s. Find its final velocity and the distance covered.

Given: u = 0, a = 4 m/s², t = 5 s

v = u + at = 0 + 4×5 = 20 m/s

s = ut + ½at² = 0 + ½×4×5² = ½×4×25 = 50 m

Q2. A bus moving at 20 m/s is brought to rest in 4 s. Find its acceleration (retardation) and stopping distance.

Given: u = 20 m/s, v = 0, t = 4 s

a = (v − u)/t = (0 − 20)/4 = −5 m/s² (negative ⇒ retardation)

Stopping distance, s = (v² − u²)/2a = (0 − 400)/(2×−5) = 40 m

Q3. A stone is dropped from a height (g = 10 m/s²). What is its velocity and the distance fallen after 3 s?

Given: u = 0, a = g = 10 m/s², t = 3 s

v = u + at = 0 + 10×3 = 30 m/s

s = ut + ½at² = 0 + ½×10×9 = 45 m

4. Equations of motion & which to use

Equation	Use it when you DON'T know…	Finds
v = u + at	displacement (s)	v, u, a or t
s = ut + ½at²	final velocity (v)	s, u, a or t
v² = u² + 2as	time (t)	v, u, a or s

Sign rule: choose a direction as positive. Speeding up → a is positive; slowing down → a is negative. For free fall, a = g = +9.8 m/s² (often taken as 10) downward.

5. Common mistakes & exam wins

"Starting from rest" means u = 0; "comes to rest" means v = 0. Half the marks are lost by mixing these up.
Always write units at every step — CBSE awards method marks even if the final number slips.
Slope of distance–time = speed; slope of velocity–time = acceleration; area under velocity–time = displacement.
Retardation is just negative acceleration — don't invent a new formula, just put a minus sign.
Convert km/h to m/s by multiplying by 5/18 before using any equation.

Frequently asked questions

What are the three equations of motion?

For uniformly accelerated motion: v = u + at, s = ut + ½at², and v² = u² + 2as.

Can displacement be zero when distance is not?

Yes. If you walk around a circular track and return to the start, your distance equals the track length but your displacement is zero, because you ended where you began.

What does the area under a velocity–time graph represent?

It represents the displacement of the object during that time interval.

How do I convert km/h into m/s?

Multiply by 5/18. For example, 72 km/h = 72 × 5/18 = 20 m/s.