Motion in a Straight Line formulas
Class 11 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 2, the special cases questions are built on, and diagrams where they help.
By Sreeraj P, M.Sc Physics · 10+ years teaching NEET and JEE
Most used formulasOther formulas and cases
1Distance, displacement, speed, velocity
- Distance ≥ |displacement|; equal only for straight-line motion without turning back. Distance never decreases or becomes negative; displacement can.
- Arc of angle $\theta$ on a circle of radius $r$: distance $r\theta$, displacement $2r\sin\frac\theta2$. Half circle: $\pi r$ and $2r$; full circle: $2\pi r$ and 0.
$$v_{\text{avg}}=\frac{\text{total distance}}{\text{total time}},\qquad \vec v_{\text{avg}}=\frac{\Delta\vec r}{\Delta t},\qquad \vec v=\frac{d\vec r}{dt}$$
$$\begin{array}{l}\displaystyle v_{\text{avg}}=\frac{\text{total distance}}{\text{total time}}\\[6pt]\displaystyle \vec v_{\text{avg}}=\frac{\Delta\vec r}{\Delta t}\\[6pt]\displaystyle \vec v=\frac{d\vec r}{dt}\end{array}$$
Average speed ≥ |average velocity|. Returning to start: average velocity 0, average speed not. Slope of chord / tangent of $x$–$t$ graph.
| Case | Average speed |
|---|---|
| Equal times at $v_1$, $v_2$, …, $v_n$ | $\dfrac{v_1+v_2+\dots+v_n}{n}$ (arithmetic mean) |
| Equal distances at $v_1$, $v_2$ | $\dfrac{2v_1v_2}{v_1+v_2}$ (harmonic mean) |
| Three equal distances | $\dfrac{3v_1v_2v_3}{v_1v_2+v_2v_3+v_3v_1}$ |
| Distances $s_i$ at speeds $v_i$ | $\dfrac{\sum s_i}{\sum s_i/v_i}$ |
| 1/3 distance at $v_0$, rest: half time at $v_1$, half at $v_2$ | $\dfrac{3v_0(v_1+v_2)}{4v_0+v_1+v_2}$ |
3 more sections and 14 formulas in the full chapter
- 2Acceleration and equations of motion9 formulas · 1 case table · 1 diagram
- 3Motion under gravity3 formulas · 1 case table
- 4Relative motion (1-D)2 formulas
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