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Newton's Laws of Motion formula sheet

Every formula in the Newton's Laws of Motion chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 32 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Newton's laws, momentum and impulse

First law
3× asked, last 2023
F⃗net=0  ⟺  v⃗=constant\vec F_{\text{net}}=0\iff\vec v=\text{constant}
Inertial frames only. Mass measures inertia.
Second law
7× asked, last 2025
F⃗net=dp⃗dt,F⃗net=ma⃗  (m constant)\vec F_{\text{net}}=\frac{d\vec p}{dt},\qquad \vec F_{\text{net}}=m\vec a\ \ (m\text{ constant})
Net external force; a vector law, so apply it to each component.
Changing mass
F=mdvdt+vdmdtF=m\frac{dv}{dt}+v\frac{dm}{dt}
Sand dropped on a moving belt: F=v dm/dtF=v\,dm/dt. Mass leaking at the body's own speed: F=m dv/dtF=m\,dv/dt.
Balloon dropping ballast
Δm=2Mag+a\Delta m=\frac{2Ma}{g+a}
Upthrust fixed: falling at aa with mass MM, then rising at aa after dropping Δm\Delta m.
Constant force
8× asked, last 2025
a⃗=F⃗m,v⃗=u⃗+a⃗t,r⃗=u⃗t+12a⃗t2\vec a=\frac{\vec F}{m},\qquad \vec v=\vec u+\vec a t,\qquad \vec r=\vec u t+\tfrac12\vec a t^2
From rest the path is straight along F⃗\vec F: x:y:z=Fx:Fy:Fzx:y:z=F_x:F_y:F_z.
Variable force
6× asked, last 2026
F⃗=md2r⃗dt2,F=mvdvdx\vec F=m\frac{d^2\vec r}{dt^2},\qquad F=mv\frac{dv}{dx}
Use v dv/dxv\,dv/dx when vv is given in terms of xx. Integrate F(t)/mF(t)/m for v⃗\vec v, then r⃗\vec r.
Falling against drag kvkv
v=mgk(1−e−kt/m)v=\frac{mg}{k}\left(1-e^{-kt/m}\right)
From rest; starts with slope gg, levels off at terminal speed mg/kmg/k.
Third law
2× asked, last 2024
F⃗AB=−F⃗BA\vec F_{AB}=-\vec F_{BA}
Same kind of force, on different bodies: the pair never cancels in one FBD.
Impulse
3× asked, last 2025
J⃗=∫F⃗ dt=Δp⃗,Favg=ΔpΔt\vec J=\int\vec F\,dt=\Delta\vec p,\qquad F_{\text{avg}}=\frac{\Delta p}{\Delta t}
Area under the FF–tt graph. A parabolic hump: (2/3)×(2/3)\times base × peak.
Force by a jet
1× asked, last 2022
F=dmdt v=ρAv2F=\frac{dm}{dt}\,v=\rho Av^2
Jet stopped dead. Bouncing straight back at vv: 2ρAv22\rho Av^2.

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Practise Newton's Laws of Motion

22 more formulas in 4 topics

Free-body diagrams and equilibrium; Connected bodies, pulleys and constraints; Non-inertial frames and pseudo force; and Springs. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Free-body diagrams and equilibrium

  • Free-body diagram5×
  • Lami's theorem4×
  • Rope pulled sideways4×
  • Smooth incline4×
  • Held by a horizontal push
  • Rope with mass3×
  • Chain between two supports1×

Connected bodies, pulleys and constraints

  • Blocks pulled together4×
  • Atwood machine6×
  • Block on a table, hanging mass6×
  • Double incline3×
  • Chain over an edge or pulley2×
  • Constraint relation4×
  • Movable pulley

Non-inertial frames and pseudo force

  • Apparent weight in a lift6×
  • Pseudo force5×
  • Bob in an accelerating vehicle1×
  • Block on an accelerating incline2×
  • Block on a free wedge1×

Springs

  • Spring force1×
  • Series, parallel and cut springs
  • Sudden cut: spring vs string

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About 70 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Newton's Laws of Motion

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