Kinematics 1-D formulas

Every formula JEE Advanced expects you to know for Kinematics 1-D, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 30
Subject: Physics
Exam: JEE Advanced
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Kinematics 1-D, every formula

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

Displacement
$Δ x = x_{f} - x_{i}$
change in position
Average velocity
$⟨ v ⟩ = \frac{Δ x}{Δ t}$
Average speed
$avg speed = \frac{total distance}{total time}$
Instantaneous velocity
$v = \frac{d x}{d t}$
Average acceleration
$⟨ a ⟩ = \frac{Δ v}{Δ t}$
Instantaneous acceleration
$a = \frac{d v}{d t}$
First equation of motion
$v = u + a t$
Second equation of motion
$s = u t + \frac{1}{2} a t^{2}$
Third equation of motion
$v^{2} = u^{2} + 2 a s$
Average-velocity equation
$s = \frac{u + v}{2} t$
Distance in nth second
$s_{n} = u + \frac{a}{2} (2 n - 1)$
Acceleration as v·dv/dx
$a = v \frac{d v}{d x}$
Free fall from rest (speed)
$v = g t$
u=0
Free fall from rest (distance)
$h = \frac{1}{2} g t^{2}$
Maximum height (vertical throw)
$H = \frac{u ^{2}}{2 g}$
Time of flight (vertical throw)
$T = \frac{2 u}{g}$
Time to fall from height h
$t = \frac{2 h}{g}$
Speed on reaching ground
$v = 2 g h$
Galileo's odd-number ratio
$s_{1} : s_{2} : s_{3} : \dots = 1 : 3 : 5 : \dots$
equal time intervals
Slope of x–t graph
$\frac{d x}{d t} = v$
Slope of v–t graph
$\frac{d v}{d t} = a$
Area under v–t graph
$\int v d t = displacement$
Area under a–t graph
$\int a d t = Δ v$
Slope of v²–x graph
$\frac{d ( v ^{2} )}{d x} = 2 a$
Relative velocity (1-D)
$v_{A B} = v_{A} - v_{B}$
Three-object throw relation
$t_{3} = t_{1} t_{2}$
up, down, dropped from same height
Distance vs displacement
$distance \geq ∣ displacement ∣$
a = f(t) integration
$\int d v = \int a d t$
a = f(x) integration
$\int v d v = \int a d x$
Speed–velocity relation
$∣ avg velocity ∣ \leq avg speed$

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Kinematics 1-D formulas

Kinematics 1-D, every formula

Displacement

Average velocity

Average speed

Instantaneous velocity

Average acceleration

Instantaneous acceleration

First equation of motion

Second equation of motion

Third equation of motion

Average-velocity equation

Distance in nth second

Acceleration as v·dv/dx

Free fall from rest (speed)

Free fall from rest (distance)

Maximum height (vertical throw)

Time of flight (vertical throw)

Time to fall from height h

Speed on reaching ground

Galileo's odd-number ratio

Slope of x–t graph

Slope of v–t graph

Area under v–t graph

Area under a–t graph

Slope of v²–x graph

Relative velocity (1-D)

Three-object throw relation

Distance vs displacement

a = f(t) integration

a = f(x) integration

Speed–velocity relation

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