Kinematics and Laws of Motion — NEET Physics

Mechanics is the largest block in NEET Physics, and it all starts here. Kinematics describes how things move — positions, velocities, accelerations — without asking why. Newton's laws supply the why: forces cause acceleration. Almost every mechanics question in the paper reduces to one of the three equations of motion or a force balance $F=ma$, so the fluency you build in this chapter pays back across projectiles, circular motion, work-energy, rotation and even fluids. We build each idea from its definition, derive the working formulas, and drill them with the exact kinds of problems NEET sets.

1. The vocabulary: scalars, vectors and the four quantities

• Distance (scalar) is the total path length; displacement (vector) is the straight-line change in position. A runner completing one lap has covered a distance of 400 m but zero displacement.
• Speed (scalar) is distance/time; velocity (vector) is displacement/time. Average speed can be non-zero while average velocity is zero.
• Acceleration is the rate of change of velocity — so a body moving at constant speed around a circle is still accelerating, because its direction (and hence velocity) changes.

This distinction is not pedantry: many NEET traps hinge on "distance vs displacement" or "speed vs velocity," especially in circular and to-and-fro motion.

2. The three equations of motion

For constant acceleration, integrating $a=\text{const}$ once and twice gives:

$v=u+at,s=ut+\frac{1}{2}a{t}^2,v^2=u^2+2as$

where $u$ is initial velocity, $v$ final velocity, $a$ acceleration, $s$ displacement, $t$ time.

• A car decelerating from 20 m/s at 4 m/s² stops in $t=20/4=5$ s and travels $s=\frac{v^2-u^2}{2a}=\frac{0-400}{-8}=50$ m.

Choose the equation that omits the quantity you neither know nor want. Need $s$ without $t$? Use $v^2=u^2+2as$. Need $v$ without $s$? Use $v=u+at$.

3. Motion under gravity

Free fall is constant-acceleration motion with $a=g\approx 9.8$ m/s² (often taken as 10 for speed), downward. Taking "up" as positive, a body thrown up at speed $u$:

$H_{\max }=\frac{u^2}{2g},t_{\text{up}}=\frac{u}{g},t_{\text{flight}}=\frac{2u}{g}$

• Thrown up at 20 m/s ($g=10$): rises $H=\frac{400}{20}=20$ m, taking 2 s up and 2 s down.

The motion is symmetric: speed at any height going up equals speed at the same height coming down, and time up equals time down.

4. Motion graphs

Graphs turn calculation into reading:

• Position–time ($x$–$t$): the slope is velocity. A straight line is uniform velocity; a curve is acceleration.
• Velocity–time ($v$–$t$): the slope is acceleration, and the area under the curve is displacement.

A NEET favourite: "displacement = area under the $v$–$t$ graph." For a body starting from rest at constant $a$, that area is a triangle, $\frac{1}{2}\cdot t\cdot (at)=\frac{1}{2}a{t}^2$ — the second equation of motion, recovered geometrically.

5. Relative velocity

The velocity of A relative to B is ${\vec{v}}_{AB}={\vec{v}}_A-{\vec{v}}_B$.

• Two trains at 60 km/h approaching each other close at $60+60=120$ km/h; moving apart, $0$.
• River–boat: to cross straight, the boat must head partly upstream so its across-stream component cancels the current.

6. Projectile motion

Gravity acts only vertically, so horizontal and vertical motions are independent, linked only by the shared time. For launch speed $u$ at angle $\theta$:

$R=\frac{u^2\sin 2\theta }{g},H=\frac{u^2{\sin }^2\theta }{2g},T=\frac{2u\sin \theta }{g}$

• Horizontal velocity $u\cos \theta$ is constant; vertical velocity starts at $u\sin \theta$ and is changed by $g$.
• Range is maximum at $\theta =45°$ ($\sin 2\theta =1$). Complementary angles (e.g. 30° and 60°) give the same range, because $\sin 2\theta =\sin (180°-2\theta )$.

Worked example 6.1. At $u=20$ m/s, $\theta =45°$: $R=\frac{400\times 1}{10}=40$ m. Worked example 6.2. At $u=20$ m/s, $\theta =30°$: $H=\frac{400\times (0.5{)}^2}{2\times 10}=\frac{100}{20}=5$ m.

7. Newton's three laws

1. First law (inertia): a body continues at rest or in uniform motion unless acted on by a net external force. Inertia is measured by mass.
2. Second law: ${\vec{F}}_{\text{net}}=m\vec{a}$ — the working equation of all dynamics. In momentum form, $\vec{F}=\frac{d\vec{p}}{dt}$.
3. Third law: to every action there is an equal and opposite reaction, acting on a different body — which is why the pair never cancels on a single object.

Rockets, walking and swimming are all third-law propulsion: push mass one way, get pushed the other.

8. Free-body diagrams and their applications

Draw every force on the chosen body, then apply $F=ma$ per direction.

Apparent weight in a lift — the normal force (what a scale reads):

$N=m(g+a)\text{(accelerating up)},m(g-a)\text{(down)},mg\text{(rest/uniform)},0\text{(free fall)}$

• A 50 kg person in a lift accelerating up at 2 m/s² ($g=10$) feels $N=50\times 12=600$ N — heavier than their 500 N true weight.

Frictionless inclined plane — the component of gravity along the slope drives the motion:

$a=g\sin \theta ,N=mg\cos \theta$

At $\theta =30°$: $a=g\sin 30°=5$ m/s².

Worked example 8.1 (free fall lift). In free fall the lift and person accelerate together at $g$, so the normal force is zero — the origin of weightlessness. This is the same physics as an orbiting astronaut.

9. Friction

Friction opposes relative sliding, up to a limit:

$f_{s,\max }={\mu }_{s}N,f_k={\mu }_{k}N({\mu }_k<{\mu }_s)$

• Static friction self-adjusts up to its maximum to prevent motion; kinetic friction is roughly constant once sliding.
• On an incline, a block just begins to slide at the angle of repose $\theta$, where $\tan \theta ={\mu }_s$.
• On a rough incline, $a=g(\sin \theta -\mu \cos \theta )$ (sliding down).

Worked example 9.1. If ${\mu }_s=1/\sqrt{3}$, the angle of repose is $\theta ={\tan }^{-1}(1/\sqrt{3})=30°$ — the steepest angle at which the block still rests.

10. Uniform circular motion

Moving in a circle at constant speed still means constant acceleration, directed inward (centripetal):

$a_c=\frac{v^2}{r}={\omega }^{2}r,F_c=\frac{m{v}^2}{r}$

• $v=10$ m/s on $r=20$ m: $a_c=100/20=5$ m/s², toward the centre.
• Banking of roads: the ideal banking angle (no friction needed) satisfies $\tan \theta =\frac{v^2}{rg}$.
• Maximum speed on a flat curve (friction supplies $F_c$): $v_{\max }=\sqrt{\mu rg}$.

Worked example 10.1. Flat curve, $\mu =0.5$, $r=20$ m, $g=10$: $v_{\max }=\sqrt{0.5\times 20\times 10}=\sqrt{100}=10$ m/s. Above this, the car skids outward.

There is no real outward "centrifugal force" in the ground frame — the inward friction/normal component is the net force; the outward feeling is inertia.

11. Impulse and conservation of momentum

$\text{Impulse}=F\Delta t=\Delta p=m\Delta v$

For an isolated system (no external force), total momentum is conserved — the backbone of collision and recoil problems.

• Gun recoil: a 4 kg gun firing a 0.02 kg bullet at 200 m/s recoils at $V=\frac{0.02\times 200}{4}=1$ m/s (opposite direction).
• Ball off a wall: a 0.2 kg ball hitting a wall at 10 m/s and rebounding at 10 m/s changes momentum by $\Delta p=0.2\times (10-(-10))=4$ kg·m/s — twice the incoming momentum, because the direction reverses.

Airbags and follow-through both exploit impulse: stretch $\Delta t$ to cut the force for the same momentum change.

12. Common traps NEET sets here

• Distance vs displacement / speed vs velocity — especially in circular or to-and-fro motion.
• Using the motion equations when $a$ is not constant — they fail entirely.
• Normal force = mg always — false on an incline ($mg\cos \theta$) or in an accelerating lift.
• Mixing horizontal and vertical in projectiles — keep them separate, joined only by time.
• Forgetting momentum reverses at a wall — $\Delta p=2mv$, not $mv$.
• Inventing a real centrifugal force in the ground frame — the net force in circular motion points inward.

13. Memory aids

• "SUVAT" — the five symbols $s,u,v,a,t$; pick the equation missing the one you don't need.
• "45 for range, complements tie" — max range at 45°, and 30°/60° share a range.
• "Up: g+a, Down: g−a, Fall: zero" — apparent weight in a lift.
• "tan θ = μ" — the angle of repose.
• "Inward is the net" — circular motion has no outward force in the ground frame.

14. Exam protocol

1. Separate distance/displacement and speed/velocity before starting.
2. Confirm constant acceleration, then pick the SUVAT equation that omits your unneeded variable.
3. For projectiles, split into horizontal (constant) and vertical (g); range peaks at 45°.
4. Always draw a free-body diagram and apply $F=ma$ per direction.
5. On inclines use $mg\sin \theta$ and $mg\cos \theta$; remember lift apparent weight $m(g\pm a)$.
6. Use $f=\mu N$ and the angle of repose $\tan \theta =\mu$.
7. Circular motion: $a_c=v^2/r$ inward; banking $\tan \theta =v^2/rg$; flat-curve $v_{\max }=\sqrt{\mu rg}$.
8. Reach for conservation of momentum in recoil/collision and impulse = Δp in force–time problems.