Kinematics 2-D formulas

Every formula JEE Advanced expects you to know for Kinematics 2-D, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas 83 practice questions

Formulas: 30
Subject: Physics
Exam: JEE Advanced
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Kinematics 2-D, every formula

30 formulas, typeset and free. Print it, or keep it open beside your practice.

Horizontal velocity component
$u_{x} = u cos θ$
Vertical velocity component
$u_{y} = u sin θ$
Time of flight (ground)
$T = \frac{2 u sin θ}{g}$
Maximum height
$H = \frac{u ^{2} sin ^{2} θ}{2 g}$
Horizontal range
$R = \frac{u ^{2} sin 2 θ}{g}$
Maximum range
$R_{m a x} = \frac{u ^{2}}{g} at θ = 4 5^{\circ}$
Trajectory equation
$y = x tan θ - \frac{g x ^{2}}{2 u ^{2} cos ^{2} θ}$
Velocity at time t
$v = u cos θ \hat{i} + (u sin θ - g t) \hat{j}$
Direction of velocity
$tan ϕ = \frac{u sin θ - g t}{u cos θ}$
Speed at highest point
$v = u cos θ$
v_y=0 there
Range–height relation
$R = 4 H cot θ$
Complementary angles
$θ and 9 0^{\circ} - θ give equal range$
Two times to reach height h
$h = \frac{g t _{1} t _{2}}{2}$
Horizontal projection: time
$T = \frac{2 H}{g}$
Horizontal projection: range
$R = u \frac{2 H}{g}$
Horizontal projection: path
$y = - \frac{g x ^{2}}{2 u ^{2}}$
Horizontal projection: angle
$tan ϕ = \frac{g t}{u}$
Projectile speed
$v = v_{x}^{2} + v_{y}^{2}$
Time perpendicular to u
$t = \frac{u}{g sin θ}$
Incline range (up)
$R = \frac{2 u ^{2} sin α cos ( α + β )}{g cos ^{2} β}$
Incline range (down)
$R = \frac{2 u ^{2} sin α cos ( α - β )}{g cos ^{2} β}$
Incline time of flight
$T = \frac{2 u sin α}{g cos β}$
Incline max range (up)
$R_{m a x} = \frac{u ^{2}}{g ( 1 + sin β )}$
Incline max-range angle
$\frac{π}{4} - \frac{β}{2} (up), \frac{π}{4} + \frac{β}{2} (down)$
Relative velocity
$v_{A B} = v_{A} - v_{B}$
Relative acceleration
$a_{A B} = a_{A} - a_{B}$
River shortest time (net speed)
$v_{m} = v_{m R}^{2} + v_{R}^{2}$
River shortest path (angle)
$θ = sin^{- 1} (\frac{v _{R}}{v _{m R}})$
River shortest path (time)
$t = \frac{d}{v _{m R}^{2} - v _{R}^{2}}$
Rain–man velocity
$v_{R m} = v_{R} - v_{m}, v_{R m} = v_{R}^{2} + v_{m}^{2}$

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Kinematics 2-D formulas

Kinematics 2-D, every formula

Horizontal velocity component

Vertical velocity component

Time of flight (ground)

Maximum height

Horizontal range

Maximum range

Trajectory equation

Velocity at time t

Direction of velocity

Speed at highest point

Range–height relation

Complementary angles

Two times to reach height h

Horizontal projection: time

Horizontal projection: range

Horizontal projection: path

Horizontal projection: angle

Projectile speed

Time perpendicular to u

Incline range (up)

Incline range (down)

Incline time of flight

Incline max range (up)

Incline max-range angle

Relative velocity

Relative acceleration

River shortest time (net speed)

River shortest path (angle)

River shortest path (time)

Rain–man velocity

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