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Rectilinear Motion formula sheet

Every formula in the Rectilinear Motion chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 38 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.

Displacement, velocity and acceleration

Distance and displacement
8× asked, last 2026
∣Δr⃗ ∣≤distance|\Delta\vec r\,|\le\text{distance}
Equal only for one-way straight motion. An extra full lap adds distance, not displacement.
Arc of a circle
5× asked, last 2025
distance=Rθ,∣Δr⃗ ∣=2Rsin⁡θ2\text{distance}=R\theta,\qquad |\Delta\vec r\,|=2R\sin\frac\theta2
θ\theta in radians at the centre. Quarter circle: R2R\sqrt2; half: 2R2R; full lap: 0.
Average speed and velocity
6× asked, last 2026
vˉ=total distancetotal time,v⃗avg=Δr⃗Δt\bar v=\frac{\text{total distance}}{\text{total time}},\qquad \vec v_{\text{avg}}=\frac{\Delta\vec r}{\Delta t}
Average speed ≥∣v⃗avg∣\ge|\vec v_{\text{avg}}|. Back at the start: zero average velocity.
Equal distances or equal times
9× asked, last 2025
vˉequal x=2v1v2v1+v2,vˉequal t=v1+v22\bar v_{\text{equal }x}=\frac{2v_1v_2}{v_1+v_2},\qquad \bar v_{\text{equal }t}=\frac{v_1+v_2}{2}
nn equal distances: vˉ=n/(1/v1+⋯+1/vn)\bar v=n/(1/v_1+\dots+1/v_n). Never the plain mean of phase speeds.
Instantaneous velocity and acceleration
8× asked, last 2025
v=dxdt,a=dvdt=d2xdt2v=\frac{dx}{dt},\qquad a=\frac{dv}{dt}=\frac{d^2x}{dt^2}
Differentiate first, put in tt last. Speed =vx2+vy2+vz2=\sqrt{v_x^2+v_y^2+v_z^2}.
Speeding up or slowing down
va>0: speeding up,va<0: slowing downva>0:\ \text{speeding up},\qquad va<0:\ \text{slowing down}
The sign of aa alone does not decide it: a<0a<0 with v<0v<0 is speeding up.
Average acceleration
2× asked, last 2023
a⃗avg=v⃗2−v⃗1Δt\vec a_{\text{avg}}=\frac{\vec v_2-\vec v_1}{\Delta t}
A vector change. A bounce reverses vv, so ∣Δv∣=v1+v2|\Delta v|=v_1+v_2.

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Practise Rectilinear Motion

31 more formulas in 4 topics

Equations of motion (uniform acceleration), Motion graphs, Motion under gravity and Variable acceleration. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Equations of motion (uniform acceleration)

  • Equations of motion9×
  • Displacement from the end velocities
  • Stopping distance and time4×
  • Displacement in the nnth second4×
  • Starting from rest7×
  • Accelerate, then brake to rest3×
  • Velocity at the midpoint1×
  • Constant acceleration in a plane2×

Motion graphs

  • Position–time graph4×
  • Velocity–time graph10×
  • Acceleration–time graph3×
  • Velocity–position graph3×
  • Graph of v2v^2 against xx2×

Motion under gravity

  • Free fall from rest10×
  • Thrown straight up8×
  • Times at a height h′h'
  • Thrown from a tower6×
  • Up, down and dropped from one point2×
  • Released from a moving body3×
  • Drops from a tap3×
  • Two bodies in free fall4×
  • Bouncing ball3×
  • Constant air drag1×
  • Smooth incline2×

Variable acceleration

  • Acceleration from v(x)v(x)4×
  • Integrating v(t)v(t) and a(t)a(t)3×
  • Time given as a function of xx2×
  • Implicit xx–tt relation2×
  • Turning points and extreme velocity4×
  • Force depending on xx or vv2×
  • Retardation proportional to speed

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