How much of JEE Main comes from Kinematics?

JEEGenie estimates about 4% of JEE Main marks come from Kinematics, based on recent papers. The share varies from year to year.

Which formulas matter most in Kinematics?

The Kinematics sheet on this page has 19 formula entries, starting with Distance vs Displacement, Speed vs Velocity, Instantaneous Velocity & Acceleration, Equations of Motion (Constant Acceleration), Graphical Analysis: v-t and x-t. Each one comes with when to use it and the trap to avoid.

What topics does Kinematics cover for JEE?

Kinematics covers Motion in a Straight Line, Graphs of Motion, Relative Velocity, Projectile Motion, Motion in a Plane.

How should I revise Kinematics before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Kinematics questions on JEEGenie.

How many previous-year questions are there on Kinematics?

JEEGenie has 453 previous-year questions on Kinematics, and this page shows a few with worked explanations.

Is practice on Kinematics free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Kinematics for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 4% of JEE Main marks come from Kinematics. This page covers 19 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Assuming motion is absolute without specifying a reference frame.

Key points to know

Frame of Reference & Rest/Motion. Motion is relative; an object's state is defined with respect to a chosen frame of reference. A frame is a coordinate system + a clock.
Distance vs Displacement. Distance is scalar (total path length), displacement is vector (shortest path from start to end). Displacement ≤ distance.
Speed vs Velocity. Speed is scalar (rate of distance), velocity is vector (rate of displacement). Average speed = total distance/total time; average velocity = displacement/time.
Instantaneous Velocity & Acceleration. Instantaneous velocity is the derivative of position; acceleration is derivative of velocity. Both are vectors.
Projectile Motion Basics. A projectile under gravity has constant horizontal velocity and constant vertical acceleration. Motion is 2D parabolic.
Uniform Circular Motion. Motion in a circle at constant speed; acceleration is centripetal (towards center) and changes direction only.
Relative Motion in 2D. Velocity of A relative to B: ${\vec{v}}_{A B} = {\vec{v}}_{A} - {\vec{v}}_{B}$ . Use vector subtraction.
Sign Convention in Kinematics. Choose a positive direction consistently. Displacement, velocity, acceleration can be positive or negative. In free fall, upward positive is common.
Calculus in Kinematics. For variable acceleration, use differentiation and integration: $v = \frac{d x}{d t}$ , $a = \frac{d v}{d t}$ , $x = \int v d t$ , $v = \int a d t$ .
Free Fall Under Gravity. Only force is gravity; acceleration is constant $g$ downward. Use equations of motion with $a = \pm g$ .
Scalars and Vectors in Kinematics. Position, displacement, velocity, acceleration are vectors. Speed, distance, time are scalars. Always treat direction.
Average vs Instantaneous Quantities. Average is over an interval; instantaneous is at a point. Use limits for instantaneous.

Formula sheet

Name	Formula	When to use
Distance vs Displacement	Displacement $\vec{s} = {\vec{r}}_{f} - {\vec{r}}_{i}$	Always distinguish; displacement is key for velocity, distance for speed.
Speed vs Velocity	$Average speed = \frac{total distance}{Δ t}$ , ${\vec{v}}_{a v g} = \frac{Δ \vec{s}}{Δ t}$	Use speed for path length, velocity for position change.
Instantaneous Velocity & Acceleration	$\vec{v} = \frac{d \vec{r}}{d t}$ , $\vec{a} = \frac{d \vec{v}}{d t} = \frac{d^{2} \vec{r}}{d t^{2}}$	When motion is described by a function of time.
Equations of Motion (Constant Acceleration)	$v = u + a t$ ; $s = u t + \frac{1}{2} a t^{2}$ ; $v^{2} = u^{2} + 2 a s$	Any problem with uniform acceleration (e.g., free fall, motion on incline).
Graphical Analysis: v-t and x-t	$v = \frac{d x}{d t}$ , $a = \frac{d v}{d t}$ , $Δ x = \int v d t$	When given graphs or asked to interpret motion from graphs.
Relative Motion in 1D	${\vec{v}}_{A B} = {\vec{v}}_{A} - {\vec{v}}_{B}$	When two objects move along the same line (e.g., overtaking, collision).
Projectile Motion Basics	$x = u_{x} t$ , $y = u_{y} t - \frac{1}{2} g t^{2}$	Any object launched near Earth's surface with only gravity.
Projectile: Time of Flight, Range, Max Height	$T = \frac{2 u \sin θ}{g}$ ; $R = \frac{u^{2} \sin 2 θ}{g}$ ; $H = \frac{u^{2} \sin^{2} θ}{2 g}$	For level ground, no air resistance.
Projectile on Inclined Plane	For incline angle $α$ , launch angle $θ$ relative to incline: $a_{x} = - g \sin α$ , $a_{y} = - g \cos α$	When projectile is launched up or down an incline.
Uniform Circular Motion	$a_{c} = \frac{v^{2}}{r} = ω^{2} r$ , $v = ω r$ , $T = \frac{2 π}{ω}$	Any object moving in a circular path at constant speed.
Non-Uniform Circular Motion	$a_{t} = \frac{d v}{d t}$ , $a_{c} = \frac{v^{2}}{r}$ , $a_{net} = \sqrt{a_{t}^{2} + a_{c}^{2}}$	When speed is not constant (e.g., vertical loop).
Relative Motion in 2D	${\vec{v}}_{A B} = {\vec{v}}_{A} - {\vec{v}}_{B}$	When two objects move in a plane (e.g., rain-man, boat-river).
River-Boat Problems	${\vec{v}}_{b g} = {\vec{v}}_{b w} + {\vec{v}}_{w g}$ ; Time to cross: $t = \frac{d}{v_{b w} \cos θ}$ ; Drift: $x = (v_{w g} - v_{b w} \sin θ) t$	Boat crossing a river with current.
Rain-Man Problems	${\vec{v}}_{r m} = {\vec{v}}_{r} - {\vec{v}}_{m}$	When a person moves in rain and needs umbrella direction.
Calculus in Kinematics	$v = \frac{d x}{d t}$ , $a = \frac{d v}{d t}$ , $Δ x = \int_{t_{1}}^{t_{2}} v d t$ , $Δ v = \int_{t_{1}}^{t_{2}} a d t$	When acceleration is a function of time, velocity, or position.
Motion Graphs: x-t, v-t, a-t Interconversion	$v = \frac{d x}{d t}$ , $a = \frac{d v}{d t}$ , $Δ x = \int v d t$ , $Δ v = \int a d t$	When given one graph and asked to sketch another or find quantities.
Free Fall Under Gravity	$v = u \pm g t$ , $s = u t \pm \frac{1}{2} g t^{2}$ , $v^{2} = u^{2} \pm 2 g s$	Any object dropped or thrown vertically near Earth.
Stopping Distance and Reaction Time	$s_{total} = v_{0} t_{r} + \frac{v_{0}^{2}}{2 a}$ (where $a$ is deceleration)	Problems involving vehicle braking or safety.
Average vs Instantaneous Quantities	$v_{a v g} = \frac{Δ x}{Δ t}$ , $v = \lim_{Δ t \to 0} \frac{Δ x}{Δ t}$	When time interval is given vs specific time.

Open the Kinematics formula page

What JEE asks

Frame of Reference & Rest/Motion. JEE often asks to identify relative motion or choose the correct frame for a problem.
Distance vs Displacement. JEE often tests with a particle moving on a curved path; find displacement magnitude.
Speed vs Velocity. JEE often gives a trip with multiple segments; compute average speed and velocity separately.
Instantaneous Velocity & Acceleration. JEE gives $x (t)$ and asks for $v (t)$ or $a (t)$ via differentiation.
Equations of Motion (Constant Acceleration). JEE often combines two equations to find unknowns; watch for sign conventions.
Graphical Analysis: v-t and x-t. JEE often gives a v-t graph and asks for displacement, acceleration, or distance traveled.
Relative Motion in 1D. JEE often asks time to meet or distance between moving objects using relative velocity.
Projectile Motion Basics. JEE often asks for time of flight, range, or maximum height.
Projectile: Time of Flight, Range, Max Height. JEE often asks for ratio of ranges or heights for different angles.
Projectile on Inclined Plane. JEE often asks for range along the incline or time of flight.
Uniform Circular Motion. JEE often asks for centripetal force or relation between $v$ , $ω$ , $T$ .
Non-Uniform Circular Motion. JEE often asks for net acceleration at a point in a vertical circle.
Relative Motion in 2D. JEE often asks for direction to hold umbrella or boat crossing river.
River-Boat Problems. JEE often asks for minimum time or minimum drift conditions.
Rain-Man Problems. JEE often asks for angle of umbrella relative to vertical.
Sign Convention in Kinematics. JEE often tests sign awareness in multi-step problems.
Calculus in Kinematics. JEE often gives $a (t)$ and asks for $v (t)$ or $x (t)$ via integration.
Motion Graphs: x-t, v-t, a-t Interconversion. JEE often gives a v-t graph and asks for acceleration at a point or total displacement.
Free Fall Under Gravity. JEE often asks for time to reach ground or height from velocity.
Stopping Distance and Reaction Time. JEE often asks for minimum distance to avoid collision.
Scalars and Vectors in Kinematics. JEE often tests vector nature in multiple-choice questions.
Average vs Instantaneous Quantities. JEE often asks for instantaneous velocity from position function.
Solving Kinematics Problems: Step-by-Step. JEE often requires combining multiple equations; systematic approach is key.

Common traps

Assuming motion is absolute without specifying a reference frame. Frame of Reference & Rest/Motion
Using distance in place of displacement in velocity calculations. Distance vs Displacement
Assuming average speed equals magnitude of average velocity. Speed vs Velocity
Forgetting that acceleration can be non-zero even when speed is constant (e.g., circular motion). Instantaneous Velocity & Acceleration
Using these for non-constant acceleration (requires calculus). Equations of Motion (Constant Acceleration)
Confusing area under v-t with distance (area gives displacement; distance is absolute area). Graphical Analysis: v-t and x-t
Sign errors: subtract velocities in correct order. Relative Motion in 1D
Assuming horizontal acceleration is non-zero. Projectile Motion Basics
Complementary angles ( $θ$ and $90^{\circ} - θ$ ) give the same range since $\sin 2 θ = \sin (180^{\circ} - 2 θ)$ ; maximum range is at $45^{\circ}$ . Projectile: Time of Flight, Range, Max Height
Using standard projectile formulas directly without adjusting for incline. Projectile on Inclined Plane
Thinking acceleration is zero because speed is constant. Uniform Circular Motion
Forgetting tangential component when speed changes. Non-Uniform Circular Motion
Adding instead of subtracting vectors. Relative Motion in 2D
Confusing angle of boat with direction of resultant velocity. River-Boat Problems

Topics in Kinematics

Motion in a Straight Line
Graphs of Motion
Relative Velocity
Projectile Motion
Motion in a Plane

Previous-year questions on Kinematics

JEEGenie has 453 previous-year questions on Kinematics. A few worked examples follow.

Year	Questions
2026	17
2025	22
2024	32
2023	38
2022	41
2021	47
2020	15
2019	54
2018	10
2017	10
2016	5
2015	4
2014	8
2013	7
2012	7
2011	6
2010	2
2009	3
2008	3
2007	4
2006	3
2005	9
2004	10
2003	8
2002	7
2001	3
2000	7
1999	6
1998	8
1997	6
1996	2
1995	5
1994	4
1993	5
1991	1
1990	1
1989	2
1988	2
1987	4
1986	4
1984	3
1983	8
1982	7
1981	2
1980	1

Question 1 easy

A person travelling on a straight line moves with a uniform velocity

v_{1}

for a distance

x

and with a uniform velocity

v_{2}

for the next

\frac{3}{2} x

distance. The average velocity in this motion is

\frac{50}{7} m / s

. If

v_{1}

5 m / s

then

v_{2} =

__________

m / s

Answer: 10

Explanation. Step 1: Total distance =

x + \frac{3}{2} x = \frac{5}{2} x

. Step 2: Time for first part:

t_{1} = \frac{x}{v_{1}} = \frac{x}{5}

. Step 3: Time for second part:

t_{2} = \frac{3 x / 2}{v_{2}} = \frac{3 x}{2 v_{2}}

. Step 4: Average velocity =

\frac{total distance}{total time} = \frac{5 x / 2}{x / 5 + 3 x / (2 v_{2})} = \frac{5}{2 (\frac{1}{5} + \frac{3}{2 v_{2}})} = \frac{50}{7}

. Step 5: Solve:

\frac{5}{2 (\frac{1}{5} + \frac{3}{2 v_{2}})} = \frac{50}{7} \Rightarrow \frac{1}{5} + \frac{3}{2 v_{2}} = \frac{7}{20} \Rightarrow \frac{3}{2 v_{2}} = \frac{3}{20} \Rightarrow v_{2} = 10

v_{2} = 10 m / s

From NTA/IIT papers: JEE Main 2025 · 2 Apr Shift 1

Question 2 hard

A block of mass

5

kg moves along the

x

-direction subject to the force

F = (- 20 x + 10)

N, with the value of

x

in metre. At time

t = 0

s, it is at rest at position

x = 1

m. The position and momentum of the block at

t = (π / 4)

s are

$- 0.5$ m, $5$ kg m/s
$0.5$ m, $0$ kg m/s
$0.5$ m, $- 5$ kg m/s
$- 1$ m, $5$ kg m/s

Answer: C

Explanation. The force is

F = - 20 x + 10 = - 20 (x - \frac{1}{2}) .

For mass

m = 5

kg,

a = \frac{F}{m} = - 4 (x - \frac{1}{2}) .

Let

u = x - \frac{1}{2}

. Then

\ddot{u} = - 4 u,

which is SHM with

ω = 2

rad/s. At

t = 0

x = 1

u (0) = 0.5

, and the block is at rest, so

\dot{u} (0) = 0

. Thus

u (t) = 0.5 \cos (2 t) .

t = \frac{π}{4}

u = 0.5 \cos (\frac{π}{2}) = 0,

x = u + 0.5 = 0.5 m .

Velocity:

\dot{u} (t) = - 0.5 \cdot 2 \sin (2 t) = - \sin (2 t) .

t = \frac{π}{4}

\dot{u} = - \sin (\frac{π}{2}) = - 1 m/s .

Thus momentum

p = m v = 5 \times (- 1) = - 5 kg m/s .

Therefore, position and momentum are

0.5 m, - 5 kg m/s

which is option **C**.

From NTA/IIT papers: JEE Advanced 2024

Question 3 easy

A particle starts with an initial velocity of

10.0 {m s}^{- 1}

along

x

-direction and accelerates uniformly at the rate of

2.0 {m s}^{- 2}

. The time taken by the particle to reach the velocity of

60.0 {m s}^{- 1}

is __________.

Answer: D

Explanation. Using v = u + at, 60 = 10 + 2t => t = 25s

From NTA/IIT papers: JEE Main 2023 · 6 Apr Shift 2

Question 4 hard

A projectile is fired from horizontal ground with speed

v

and projection angle

θ

. When the acceleration due to gravity is

g

, the range of the projectile is

d

. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is

g^{'} = \frac{g}{0.81}

, then the new range is

d^{'} = n d

. The value of

n

is ______.

Answer: 0.95

Explanation. We know the usual range is

d = \frac{v^{2} \sin 2 θ}{g} .

At the highest point, the horizontal velocity is

v_{x} = v \cos θ,

and the height is

H = \frac{v^{2} \sin^{2} θ}{2 g} .

In the new region, the vertical acceleration becomes

g^{'} = \frac{g}{0.81} .

From the highest point, the time to fall to the ground is found from

H = \frac{1}{2} g^{'} t^{' 2} \Rightarrow \frac{v^{2} \sin^{2} θ}{2 g} = \frac{1}{2} \cdot \frac{g}{0.81} t^{' 2} .

This simplifies to

t^{' 2} = \frac{0.81 v^{2} \sin^{2} θ}{g^{2}} \Rightarrow t^{'} = \frac{0.9 v \sin θ}{g} .

The time to reach the highest point in the first region was

t_{up} = \frac{v \sin θ}{g} .

Total time of flight in the new situation:

T^{'} = t_{up} + t^{'} = \frac{v \sin θ}{g} + \frac{0.9 v \sin θ}{g} = \frac{1.9 v \sin θ}{g} .

The horizontal range is

d^{'} = v \cos θ \cdot T^{'} = v \cos θ \cdot \frac{1.9 v \sin θ}{g} = 1.9 \cdot \frac{v^{2} \sin θ \cos θ}{g} .

Since

\frac{v^{2} \sin 2 θ}{g} = d and \sin 2 θ = 2 \sin θ \cos θ,

we have

\frac{v^{2} \sin θ \cos θ}{g} = \frac{d}{2} .

Thus

d^{'} = 1.9 \cdot \frac{d}{2} = 0.95 d .

n = 0.95.

0.95

From NTA/IIT papers: JEE Advanced 2022

Frequently asked questions

How much of JEE Main comes from Kinematics?: JEEGenie estimates about 4% of JEE Main marks come from Kinematics, based on recent papers. The share varies from year to year.
Which formulas matter most in Kinematics?: The Kinematics sheet on this page has 19 formula entries, starting with Distance vs Displacement, Speed vs Velocity, Instantaneous Velocity & Acceleration, Equations of Motion (Constant Acceleration), Graphical Analysis: v-t and x-t. Each one comes with when to use it and the trap to avoid.
What topics does Kinematics cover for JEE?: Kinematics covers Motion in a Straight Line, Graphs of Motion, Relative Velocity, Projectile Motion, Motion in a Plane.
How should I revise Kinematics before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Kinematics questions on JEEGenie.
How many previous-year questions are there on Kinematics?: JEEGenie has 453 previous-year questions on Kinematics, and this page shows a few with worked explanations.
Is practice on Kinematics free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.