• Distance vs Displacement: Distance = actual path length; Displacement = shortest straight-line joining start and finish. Displacement can be zero even if distance is not (e.g., one full round of a circular track).
• Speed & Velocity: \( \text{Speed}=\dfrac{\text{distance}}{\text{time}} \), \( \text{Velocity}=\dfrac{\text{displacement}}{\text{time}} \) (vector). Units (SI): m/s.
• Acceleration: \( a=\dfrac{\Delta v}{\Delta t}=\dfrac{v-u}{t} \). Positive (speeding up), negative/deceleration (slowing), or zero.
• Uniform motion: equal distances in equal times ⇒ distance–time graph is a straight line.
• Velocity–time graph: for constant velocity, horizontal line; area under the graph gives distance.
• Uniform acceleration: velocity–time graph is a straight line with slope \(a\); distance = area under the graph.

• Momentum: \( p=mv \) (vector). Law of conservation: In absence of external force, total momentum of a system is constant.
• Equations of motion (straight-line with uniform \(a\)):
  \( v=u+at \),   \( s=ut+\tfrac12 at^2 \),   \( v^2=u^2+2as \)
• Uniform circular motion: Speed constant, direction changes ⇒ accelerated motion; speed \( v=\dfrac{2\pi r}{t} \). Direction of motion at any point is along the tangent.
• Friction: Opposes motion; useful in walking/braking; produces heat.

1) Define motion with an example.

Change of position w.r.t surroundings. Example: flight of a bird, a moving bus.

2) Differentiate distance and displacement with a lap of a circular track.

One lap: distance \(=2\pi r\); displacement \(=0\) (start and end coincide).

3) Give SI units of speed and velocity.

Both are in m/s; velocity is vector, speed is scalar.

4) State conditions when velocity changes.

Change in speed, change in direction, or both.

5) What is uniform motion?

Equal distances in equal time intervals along a straight path.

6) Define acceleration; write its formula.

Rate of change of velocity: \(a=(v-u)/t\).

7) What is inertia? On what does it depend?

Resistance to change of state; depends on mass.

8) State Newton’s third law.

Every action has an equal and opposite reaction; acts on different bodies.

9) Write the three equations of motion.

\(v=u+at\), \(s=ut+\tfrac12 at^2\), \(v^2=u^2+2as\).

10) Define momentum and its unit.

\(p=mv\); unit kg·m/s.

11) State the law of conservation of momentum.

In an isolated system, total momentum remains constant.

12) Why are seat belts helpful?

Increase stopping time ⇒ reduces impact force (impulse concept).

13) Example where displacement is less than distance.

Going via a curved road between two points; straight-line is shorter.

14) What is uniform circular motion?

Motion at constant speed in a circle; accelerated due to changing direction.

15) Direction of velocity in circular motion?

Along the tangent to the circle at that point.

16) Give two uses of friction.

Walking and braking/tyre grip.

17) Define impulse; relation with momentum.

\(J=Ft=\Delta p\).

18) What do you get from the area under a \(v\)-\(t\) graph?

Displacement (or distance for one-direction motion).

19) What is deceleration?

Negative acceleration; velocity decreases with time.

20) State when speed equals magnitude of velocity.

Straight-line motion without change of direction.

1) Explain with data how average speed is computed.

Average speed \(=\dfrac{\text{total distance}}{\text{total time}}\). Add distances of each segment; divide by total time.

2) A girl jogs 600 m east and 800 m west. Find distance and displacement.

Distance \(=1400\) m; displacement \(=200\) m west.

3) When is acceleration zero?

When velocity is constant (both magnitude and direction unchanged).

4) Why does a bus passenger jerk backward when the bus starts?

Due to inertia of rest—upper body tends to remain at rest.

5) Why do athletes run on sand to train?

Higher friction & energy demand strengthens muscles; better grip.

6) State the vector/scalar nature of distance, displacement, speed, velocity, acceleration.

Scalars: distance, speed. Vectors: displacement, velocity, acceleration.

7) Why are airbags effective?

Increase impact time \(t\), so \(F=\Delta p/t\) decreases.

8) A ball thrown up returns to hand. Comment on displacement.

Final equals initial position ⇒ displacement \(=0\) (distance ≠ 0).

9) State any two limitations of using only distance-time graph.

Doesn’t show direction; cannot directly give acceleration (needs slope change).

10) Write two everyday pairs of action–reaction.

Walking (foot on ground ⇄ ground on foot); swimming (hand on water ⇄ water on hand).

11) Why is it harder to stop a loaded cart than an empty one?

More mass ⇒ more momentum/inertia ⇒ greater force required.

12) Distinguish uniform and non-uniform acceleration.

Uniform: equal velocity changes in equal times; Non-uniform: unequal changes.

13) State relation between slope of \(v\)-\(t\) graph and acceleration.

Slope \(=\dfrac{\Delta v}{\Delta t}=a\).

14) Why does a gun recoil?

Momentum conservation: forward bullet momentum equals backward gun momentum.

15) Write expression of speed in uniform circular motion.

\(v=\dfrac{2\pi r}{T}\) where \(T\) is time for one round.

16) Show how \(s\) is area under \(v\)-\(t\) straight line.

Area of trapezium: \(s=\tfrac{(u+v)}{2}\,t\), which gives \(s=ut+\tfrac12 at^2\).

17) Explain balanced vs unbalanced forces with tug-of-war.

Equal pulls ⇒ no motion (balanced). Unequal ⇒ net pull ⇒ motion towards larger force.

18) Why are sharp turns taken at lower speeds?

Direction changes quickly; at high speed required friction/centripetal force may be insufficient.

19) A sprinter goes from 0 to 10 m/s in 2 s. Calculate acceleration.

\(a=(10-0)/2=5\ \text{m/s}^2\).

20) Write two factors that affect friction.

Nature/roughness of surfaces and normal reaction (effective pressing force).

Using \(v=u+at\), \(s=ut+\tfrac12 at^2\), \(v^2=u^2+2as\).

u (m/s)	a (m/s²)	t (s)	v = u + at (m/s)
2	4	5	\(v=2+4\times5=22\)
3	5	4	\(v=3+5\times4=23\)

u (m/s)	a (m/s²)	t (s)	\(s=ut+\tfrac12 at^2\) (m)
5	2	20	\(5(20)+\tfrac12\cdot2\cdot20^2=100+400=500\)
12	7	4	\(12(4)+\tfrac12\cdot7\cdot4^2=48+56=104\)

u (m/s)	a (m/s²)	s (m)	\(v^{2}=u^{2}+2as\) ⇒ \(v\) (m/s)
4	3	92	\(v=\sqrt{4^2+2\cdot3\cdot92}=\sqrt{16+552}=\sqrt{568}\approx23.83\)
5	4	8.4	\(v=\sqrt{5^2+2\cdot4\cdot8.4}=\sqrt{25+67.2}=\sqrt{92.2}\approx9.60\)

a) A freely falling object has uniform acceleration.

Near Earth’s surface, gravitational acceleration \(g\) is nearly constant (\(\approx 9.8\,\text{m/s}^2\)) ⇒ uniform acceleration downward.

b) Action and reaction do not cancel each other.

They act on different bodies simultaneously; hence they cannot cancel on the same body.

c) Easier to stop a tennis ball than a cricket ball at same speed.

Cricket ball has larger mass ⇒ higher momentum \(p=mv\) ⇒ needs larger impulse (force × time) to stop.

d) Velocity of an object at rest is considered uniform.

Magnitude and direction are constant (both zero); hence acceleration \(=0\).

1) Walking

Foot pushes ground backward (action); ground pushes foot forward (reaction) ⇒ motion.

2) Jumping onto sand pit

Longer stopping time in sand ⇒ smaller force (impulse) ⇒ safer landing (Second law).

3) Bus start/stop jerk

Inertia (First law): body resists state change, causing backward/forward jerk.

4) Recoil of gun

Bullet forward momentum equals gun’s backward momentum (Third law & momentum conservation).

5) Rocket launch

Hot gases expelled backward; rocket gets equal and opposite thrust forward (Third law).

a) An object moves 18 m in first 3 s, 22 m in next 3 s, 14 m in last 3 s. Average speed?

Total distance \(=18+22+14=54\text{ m}\). Total time \(=9\text{ s}\).
Average speed \(=\dfrac{54}{9}=6\,\text{m/s}\).

b) A 16 kg object moves with \(a=3\,\text{m/s}^2\). Find applied force. If the same force acts on 24 kg, find its acceleration.

\(F=ma=16\times3=48\,\text{N}\). For 24 kg, \(a=\dfrac{F}{m}=\dfrac{48}{24}=2\,\text{m/s}^2\).

c) A 10 g bullet at \(1.5\,\text{m/s}\) embeds into a 90 g plank at rest. Find common velocity after collision.

\(m_1=0.01\,\text{kg},\ m_2=0.09\,\text{kg}\).
\(v=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}=\dfrac{0.01\times1.5+0}{0.10}=0.15\,\text{m/s}\).

d) A person swims 100 m in 40 s, 80 m in next 40 s, 45 m in last 20 s. Average speed?

Total distance \(=225\,\text{m}\), total time \(=100\,\text{s}\).
Average speed \(=\dfrac{225}{100}=2.25\,\text{m/s}\).

1) One round of a circular field of radius \(100\) m: distance and displacement?

Distance \(=2\pi r=200\pi\ \text{m}\approx 628.3\ \text{m}\). Displacement \(=0\).

2) Plane taxies with \(a=3.2\,\text{m/s}^2\) for \(t=30\) s. Distance covered?

\(s=ut+\tfrac12 at^2=0+\tfrac12\times3.2\times30^2=1440\,\text{m}\).

3) Kangaroo jumps vertically to \(s=2.5\) m. Find \(u\) (take \(v=0\) at top).

\(v^2=u^2+2as\Rightarrow 0=u^2-2(9.8)(2.5)\Rightarrow u=7\,\text{m/s}\).

4) Motorboat from rest to \(v=15\,\text{m/s}\) in \(5\) s: \(a\) and \(s\)?

\(a=(15-0)/5=3\,\text{m/s}^2\); \(s=\tfrac12 at^2=\tfrac12\times3\times25=37.5\,\text{m}\).

Is the person next to you in a bus in motion?

Relative to you: at rest; relative to road/trees: in motion.

Which examples show motion: bird flight, stationary train, flying leaves, stone on hill?

Motion: bird, flying leaves. No motion: stationary train, stone (w.r.t. ground).

Who takes less time—Sheetal via Sangeeta (two legs) or Prashant straight—if both speeds equal?

Prashant (straight path is shortest displacement), so less time at same speed.