Is it correct to say: Using km/h in equations of motion directly?

Always convert to m/s (multiply km/h by 5/18). Otherwise units mismatch.

Is it correct to say: Taking retardation as positive?

Retardation is negative acceleration. Substitute with a minus sign in equations.

Is it correct to say: Equating distance and displacement in circular or curved paths?

In a full circle, distance = 2πr but displacement = 0.

Is it correct to say: Applying equations of motion when acceleration is not uniform?

The three equations only apply for constant a. For variable a, use calculus or graphical methods.

Is it correct to say: Using s_n formula for total distance in n seconds?

s_n = u + a(2n−1)/2 is only for the nth second (between t = n−1 and t = n).

Is it correct to say: Forgetting to square u in third equation?

v² = u² + 2as, not v = u + 2as.

Motion — Uniform and Uniformly Accelerated

Distance, displacement, speed, velocity, acceleration, equations of motion — Maharashtra Board Class 10 Physics

📐 8 formulas✏️ 3 examples🎯 5 practice⚖️ 4 marks🏫 Maharashtra State Board📚 Class 10✓ 2025–26 syllabus

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Board Exam Tips

→The three equations of motion must be derived graphically — 3-mark question every board.
→Draw velocity–time graphs neatly; label axes and slope. Marks depend on labelling.
→Distinguish distance (scalar) vs displacement (vector) in a 1-mark answer.
→Numericals on train/car acceleration are SSC staples — practise unit conversions (km/h ↔ m/s).
→Do not forget: uniform velocity ⇒ a = 0, so v² = u², s = ut.

📊 Diagram

Velocity–time graph for uniformly accelerated motion

📐 Formulas(8)

Average Speed

Average speed = \frac{Total distance}{Total time}

Average Velocity

v_{a v g} = \frac{Displacement}{Time}

Acceleration★ Board fav

a = \frac{v - u}{t}

First Equation of Motion★ Board fav

v = u + a t

Second Equation of Motion★ Board fav

s = u t + \frac{1}{2} a t^{2}

Third Equation of Motion

v^{2} = u^{2} + 2 a s

Displacement in nth second

s_{n} = u + \frac{a}{2} (2 n - 1)

Uniform Circular Motion — Speed

v = \frac{2 π r}{T}

✏️ Solved Examples

1Solved Exampleeasy4 steps

A car accelerates uniformly from 18 km/h to 36 km/h in 5 s. Calculate (i) the acceleration and (ii) the distance covered.

Convert speeds to m/s

u = 18 \times \frac{5}{18} = 5 m/s, v = 36 \times \frac{5}{18} = 10 m/s

2Solved Exampleboard4 steps

A train travelling at 72 km/h is brought to rest in 20 s. Find the retardation and the distance travelled before stopping.

Convert 72 km/h to m/s

u = 72 \times \frac{5}{18} = 20 m/s, v = 0, t = 20 s

3Solved ExampleHOTS4 steps

Two cars A and B start together from the same point. A moves with constant speed 20 m/s while B accelerates from rest at 2 m/s². When and where will B overtake A?

Distance covered by A in t seconds

s_{A} = 20 t

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Using km/h in equations of motion directly
✓Always convert to m/s (multiply km/h by 5/18). Otherwise units mismatch.
2
Taking retardation as positive
✓Retardation is negative acceleration. Substitute with a minus sign in equations.
3
Equating distance and displacement in circular or curved paths
✓In a full circle, distance = 2πr but displacement = 0.
4
Applying equations of motion when acceleration is not uniform
✓The three equations only apply for constant a. For variable a, use calculus or graphical methods.
5
Using s_n formula for total distance in n seconds
✓s_n = u + a(2n−1)/2 is only for the nth second (between t = n−1 and t = n).
6
Forgetting to square u in third equation
✓v² = u² + 2as, not v = u + 2as.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
A body starts from rest and accelerates at 4 m/s² for 6 s. Find its final velocity and distance travelled.
Q2
A cyclist covers 400 m in 20 s. What is his average speed in km/h?
Q3
A ball thrown up returns to the thrower's hand in 6 s. Find initial velocity and maximum height. (g = 10 m/s²)
Q4
A car accelerates from rest at 5 m/s². What distance does it cover in the 4th second?
Q5
A body moves with uniform velocity 15 m/s. What is its acceleration and distance in 8 s?

📝 Notes

Motion — Maharashtra SSC

Motion is where kinematics begins. The SSC board tests conceptual clarity (scalar vs vector) as well as graphical derivations. Unlike CBSE where motion is covered in Class 9, the Maharashtra Board revisits it briefly in Class 10 alongside Laws of Motion.

Scalars and vectors

Scalar: only magnitude — distance, speed, time, mass.
Vector: magnitude and direction — displacement, velocity, acceleration, force.

Types of motion

| Type | Feature | |---|---| | Uniform | Equal distances in equal intervals; a = 0 | | Non-uniform | Unequal distances; a ≠ 0 | | Uniformly accelerated | a = constant, non-zero | | Circular | Direction of velocity keeps changing |