Motion is relative: An object is in motion if its position changes w.r.t. surroundings; otherwise at rest.

Distance vs Displacement: Distance is the actual path length (scalar). Displacement is the shortest straight line from start to finish with direction (vector).

Speed & Velocity: \( \text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\) (scalar), \( \text{Velocity}=\dfrac{\text{Displacement}}{\text{Time}}\) (vector). Units (SI): m/s.

Acceleration: \( a=\dfrac{v-u}{t} \) (m/s²). Positive → speed up; Negative (deceleration) → slow down; Zero → uniform velocity.

Uniform / Non-uniform motion: Equal / unequal distances in equal times. Distance-time graph: straight line for uniform, curved for non-uniform.

Velocity-time graph: Area under the curve = displacement. Slope = acceleration.

Equations of motion: \(v=u+at,\quad s=ut+\tfrac12 at^2,\quad v^2=u^2+2as\)

Newton’s 1st Law (Inertia): Body remains at rest/uniform motion unless acted upon by an external unbalanced force.

Newton’s 2nd Law: \( F = m a \). Also \( F = \dfrac{\Delta p}{\Delta t} \), where \(p=mv\).

Newton’s 3rd Law: For every action, there is an equal and opposite reaction (on different bodies, act simultaneously).

Momentum & its conservation: \( p=mv \). In an isolated system (no external force), total momentum before = total momentum after collision.

Uniform circular motion: Speed constant, direction changes → acceleration towards center (centripetal). Speed on circle of radius \(r\) in time \(t\): \( v=\dfrac{2\pi r}{t}\).

Friction: Opposes motion; enables walking/braking; produces heat; can be useful or a loss depending on context.

1) SI unit of force?

Newton (N). \(1\,\text{N}=1\,\text{kg}\cdot\text{m}/\text{s}^2\).

2) Formula for momentum?

\(p=mv\). Vector quantity in direction of velocity.

3) Quantity with direction: speed or velocity?

Velocity. Speed has no direction (scalar).

4) Opposing force between surfaces?

Friction. Acts opposite to relative motion.

5) Law stating inertia?

Newton’s First Law.

6) Relation between force, mass and acceleration?

\(F=ma\). Basis of dynamics.

7) Product of force and time?

Impulse. \(J=F\Delta t=\Delta p\).

8) Unit of momentum?

kg·m/s.

9) Shortest straight-line measure from start to end?

Displacement.

10) Motion with equal distances in equal times?

Uniform motion.

11) Graph with slope = acceleration?

Velocity-time graph.

12) If net force is zero, acceleration is?

Zero. Velocity constant.

13) SI unit of acceleration?

m/s².

14) Equal and opposite forces law?

Newton’s Third Law.

15) Seat belts reduce injury by increasing?

Time of impact. Hence lowers force (impulse idea).

16) In uniform circular motion, which changes: speed or velocity?

Velocity. Direction changes continuously.

17) Area under v–t graph?

Displacement.

18) Slope of s–t graph in uniform motion?

Constant. Equal to speed.

19) Net (resultant) of balanced forces?

Zero.

20) Condition for momentum conservation?

No external force. System isolated.

1) Define motion.

Change in position with time relative to surroundings.

2) Define distance and displacement.

Distance: total path; Displacement: shortest straight-line with direction.

3) Write the SI units of distance, displacement and time.

m, m, s respectively.

4) Define speed and velocity.

Speed \(= \dfrac{\text{distance}}{\text{time}}\); Velocity \(= \dfrac{\text{displacement}}{\text{time}}\).

5) Define acceleration.

Rate of change of velocity: \(a=\dfrac{v-u}{t}\).

6) When are speed and velocity equal in magnitude?

In straight-line motion without change of direction.

7) What is uniform acceleration?

Equal change in velocity in equal time intervals.

8) State Newton’s First Law.

A body remains at rest/uniform motion unless unbalanced force acts.

9) State Newton’s Second Law mathematically.

\(F=ma=\dfrac{\Delta p}{\Delta t}\).

10) State Newton’s Third Law.

Every action has an equal and opposite reaction.

11) Define momentum with unit.

\(p=mv\); unit kg·m/s.

12) What is impulse?

Change in momentum: \(J=\Delta p=F\Delta t\).

13) Why are airbags used in cars?

Increase stopping time → reduces force on passengers.

14) Give two uses of friction.

Walking and braking—provides grip and stopping force.

15) What remains constant in circular motion: speed or velocity?

Speed (if uniform); velocity changes due to direction.

16) What does area under v–t graph represent?

Displacement.

17) What is deceleration?

Negative acceleration; velocity decreases with time.

18) Condition for zero acceleration but non-zero velocity?

Motion with constant velocity (no net force).

19) State any example of action–reaction.

Gun recoil; walking—foot pushes ground, ground pushes foot.

20) Write the three kinematic equations.

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

1) Why is motion called relative?

Because it is judged with respect to a chosen reference frame. A passenger may be at rest w.r.t. the bus but in motion w.r.t. the road.

2) Differentiate distance and displacement with an example.

Around a 400 m track, one lap: distance = 400 m, displacement = 0 (start = finish).

3) Explain average speed vs instantaneous speed.

Average = total distance / total time; instantaneous = speed at a particular moment (speedometer reading).

4) Give three ways to change velocity.

(i) Change speed, (ii) Change direction, (iii) Change both speed and direction.

5) State and explain inertia of rest with a daily example.

A body resists change of rest; dust falls off a carpet when jerked.

6) What is meant by unbalanced force?

Resultant force ≠ 0; causes change in state of motion (accelerates the body).

7) Why do athletes lower hands while catching a ball?

Increase time of impact → reduces force (impulse) → safer catch.

8) Write SI units of speed, velocity, acceleration, force.

m/s, m/s, m/s², Newton respectively.

9) Define uniform circular motion and its acceleration direction.

Motion with constant speed on a circle; acceleration is towards the center (centripetal).

10) Why does a gun recoil?

Momentum conservation: forward bullet momentum equals backward gun momentum.

11) State law of conservation of momentum.

In absence of external force, total momentum of a system remains constant.

12) What information do you get from slope of s–t graph?

Slope gives speed (or velocity in 1-D).

13) What does area under a v–t graph give for non-uniform motion?

Still displacement—the area can be computed by geometry/integration.

14) Give two examples where friction is useful and two where it’s a nuisance.

Useful: walking, braking. Nuisance: wear & heat in machines, energy loss.

15) Why is a thick sand bed placed for high jumpers?

To increase stopping time and reduce force on the body (impulse concept).

16) A body moves with constant speed but changing velocity—explain.

Possible in circular motion where direction (hence velocity) changes continuously.

17) Why don’t action and reaction cancel each other?

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

18) What is average velocity for a round trip back to the start?

Zero, because net displacement is zero.

19) Define deceleration with an example.

Negative acceleration, e.g., car braking from \(20\) m/s to \(0\) m/s.

20) Write expressions to find displacement from a v–t graph for (i) uniform velocity (ii) uniform acceleration.

(i) Rectangle area \(=vt\). (ii) Trapezium area \(=\tfrac12 (u+v)t\).

1) Distance vs Displacement

Distance: total path (scalar), ≥ displacement. Displacement: shortest straight-line from start to end (vector), can be zero even if distance ≠ 0.

2) Uniform vs Non-uniform motion

Uniform: equal distances in equal times; s–t graph is straight line. Non-uniform: unequal distances in equal times; s–t graph is curved.

1) Using \(v=u+at\)

Given \(u=2\,\text{m/s},\ a=4\,\text{m/s}^2,\ t=3\,\text{s}\) ⇒ \(v=u+at=2+4\times3=14\,\text{m/s}\).

Given \(u=5\,\text{m/s},\ a=2\,\text{m/s}^2,\ t=20\,\text{s}\) ⇒ \(v=5+2\times20=45\,\text{m/s}\).

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2) Using \(s=ut+\tfrac12 at^2\)

If \(u=12\,\text{m/s},\ a=7\,\text{m/s}^2,\ t=4\,\text{s}\) ⇒ \(s=12\cdot4+\tfrac12\cdot7\cdot4^2=48+56=104\,\text{m}\).

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3) Using \(v^2=u^2+2as\)

If \(u=4\,\text{m/s},\ a=3\,\text{m/s}^2,\ s=92\,\text{m}\) ⇒ \(v=\sqrt{4^2+2\cdot3\cdot92}=\sqrt{16+552}=\sqrt{568}\approx 23.83\,\text{m/s}\).

1) The minimum distance between the start and finish points is called …

Displacement — shortest straight-line from start to end.

2) Deceleration is … acceleration.

Negative acceleration — velocity decreases with time.

3) In uniform circular motion, its … changes at every point.

Velocity (direction changes though speed may remain constant).

4) During collision … remains constant (if isolated).

Total momentum — law of conservation of momentum.

5) The working of a rocket depends on Newton’s … law.

Third law — action (eject gases) & reaction (thrust).

1) Object falling freely has uniform acceleration.

In absence of significant air resistance, only gravity acts → constant \(g\approx 9.8\,\text{m/s}^2\) downward.

2) Action and reaction do not cancel each other.

They act on different bodies simultaneously; net force on each body is not zero in general.

3) Easier to stop a tennis ball than a cricket ball (same velocity).

Cricket ball has larger mass → larger momentum \(p=mv\) → requires greater impulse to stop.

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

It is constant (zero) with time; acceleration is zero.

List any five with explanation.

(1) Seat belt in a car (First law & impulse).
(2) Rocket launch (Third law & momentum conservation).
(3) Kicking a football vs a stone (Second law: \(a\propto 1/m\)).
(4) Tug of war (Unbalanced force moves rope).
(5) Walking (Third law: ground reaction propels forward; friction provides grip).

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

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

b) A 16 kg object moves with \(a=3\ \text{m/s}^2\). Find applied force. If same force acts on 24 kg, find 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 bullet \(m_1=10\ \text{g}=0.01\ \text{kg}\) at \(u_1=1.5\ \text{m/s}\) embeds in a plank \(m_2=90\ \text{g}=0.09\ \text{kg}\) at rest. Common velocity?

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

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 \(=100\ \text{s}\).
\(\displaystyle \text{Average speed}=\frac{225}{100}=2.25\ \text{m/s}\).

1) Acceleration of a body: \(u=0,\ v=15\ \text{m/s},\ t=5\ \text{s}\).

\(\displaystyle a=\frac{v-u}{t}=\frac{15-0}{5}=3\ \text{m/s}^2\). Distance: \(s=ut+\tfrac12 at^2=\tfrac12\cdot3\cdot5^2=37.5\ \text{m}\).

2) Kangaroo jumps vertically \(s=2.5\ \text{m}\). Find \(u\) (take \(g=9.8\ \text{m/s}^2\)).

At top \(v=0\). Use \(v^2=u^2+2as\) with \(a=-g\): \(0=u^2-2\cdot9.8\cdot2.5\Rightarrow u=\sqrt{49}=7\ \text{m/s}\).

3) Cannon momentum: mass \(=500\ \text{kg}\), recoil speed \(=0.25\ \text{m/s}\).

\(p=mv=500\times0.25=125\ \text{kg·m/s}\).

4) Two balls \(m_1=0.05\ \text{kg},\ u_1=3\ \text{m/s};\ m_2=0.1\ \text{kg},\ u_2=1.5\ \text{m/s}\). After collision \(v_1=2.5\ \text{m/s}\). Find \(v_2\).

\(m_1u_1+m_2u_2=m_1v_1+m_2v_2\Rightarrow 0.15+0.15=0.125+0.1v_2\Rightarrow v_2=\dfrac{0.3-0.125}{0.1}=1.75\ \text{m/s}\).

1) Which show motion: bird in flight, stationary train, leaves flying, stone lying?

Bird in flight ✅, leaves flying ✅ are in motion; stationary train and stone at rest (w.r.t. ground).

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

At rest relative to you; in motion relative to the road—motion is relative.

3) Who reaches earlier: Sheetal via detour (same speed) or Prashant straight?

Prashant—shorter displacement at same speed ⇒ less time.

4) Effect of speed/direction changes on velocity while riding a bike?

Velocity changes if (i) speed changes, (ii) direction changes, or (iii) both change.