Class 11 Physics · Gujarat Board, CBSE, GUJCET and JEE
Kinematics describes motion without asking what caused it. The three equations of motion and the projectile results here reappear in laws of motion, in circular motion, and in every entrance paper you will sit for the next two years, so they are worth over-learning.
18 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
| What | Formula | Symbols and notes |
|---|---|---|
| First equation | v = u + at | u initial velocity, v final velocity, a acceleration, t time |
| Second equation | s = ut + ½at² | s is displacement, not distance travelled |
| Third equation | v² = u² + 2as | use it when time is not given and not asked |
| Displacement in the nth second | sn = u + (a/2)(2n − 1) | the displacement during the nth second alone, not the first n seconds |
| Average velocity | vav = (u + v)/2 | valid only for uniform acceleration |
| What | Formula | Symbols and notes |
|---|---|---|
| Taking up as positive | v = u − gt, h = ut − ½gt², v² = u² − 2gh | g = 9.8 m s−2 downwards |
| Maximum height | H = u²/2g | at the top v = 0, but a is still g |
| Time to the top | t = u/g | time up equals time down for the same level |
| Total time of flight | T = 2u/g | for a body thrown up and returning to the same point |
| What | Formula | Symbols and notes |
|---|---|---|
| Time of flight | T = 2u sinθ/g | θ is the angle of projection from the horizontal |
| Maximum height | H = u² sin²θ/2g | vertical velocity is zero at the top, horizontal velocity is not |
| Horizontal range | R = u² sin2θ/g | maximum when θ = 45° |
| Equal ranges | θ and (90° − θ) give the same range | for example 30° and 60° |
| Path equation | y = x tanθ − gx²/(2u² cos²θ) | a parabola |
| Horizontal projection from a height h | T = √(2h/g), R = u√(2h/g) | the time of fall does not depend on the horizontal speed |
| What | Formula | Symbols and notes |
|---|---|---|
| Relative velocity | vAB = vA − vB | velocity of A as seen by B |
| River crossing, shortest time | t = d/vb, drift = vrd/vb | head straight across; d is river width |
| River crossing, shortest path | sinθ = vr/vb, t = d/√(vb² − vr²) | aim upstream at angle θ |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Memory hooks
“SUVAT”
What the letters in the equations of motion mean
s displacement, u initial velocity, v final velocity, a acceleration, t time. Every problem gives you three of them and asks for a fourth; pick the equation that leaves out the one you neither have nor want.
“Horizontal is lazy, vertical does the work”
Projectile motion
Horizontal velocity never changes because there is no horizontal force. Everything interesting, the rise, the fall, the time, comes from the vertical part.
“30 and 60 land together”
Equal ranges
Two angles adding to 90° give the same range. The larger angle simply spends longer in the air and less time moving forward.
Where marks go
Test yourself
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