Kinematics — Class 11 ISC Physics revision notes
A 5-page visual revision sheet for Kinematics, written for Class 11 ISC Physics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Kinematics in one look
motion described with calculus, and vectors put on a plane
Position, and the words that are not interchangeable
- motion is always relative to a frame of reference, so rest and motion are statements about a frame and never about a body alone
- distance is the path length and is never negative; displacement is the straight line from start to finish and carries a direction
- speed is distance over time and velocity is displacement over time, so a body can move at steady speed with changing velocity
- average velocity uses the whole interval, instantaneous velocity is the limit as that interval shrinks to zero, which is where calculus enters
The calculus this course actually needs
- differentiation is a rate of change: velocity is the rate of change of position and acceleration the rate of change of velocity, so v = dx/dt and a = dv/dt
- the chain of it: a = dv/dt = d^2x/dt^2, and a = v dv/dx when acceleration is wanted in terms of position rather than time
- integration is the reverse: displacement is the integral of velocity over time, and velocity the integral of acceleration
- the syllabus names the derivatives to know: x^n, sin x, cos x, e^x and ln x, and the integral of x^n dx. Both definite and indefinite integrals are mentioned, and elementary calculus is not evaluated beyond this
The five derivatives and the one integral named
| Function | Derivative | Function | Derivative |
|---|---|---|---|
| x^n | n x^n-1 | e^x | e^x |
| sin x | cos x | ln x | 1/x |
| cos x | -sin x | constant | 0 |
| integral of x^n dx | x^n+1 / (n+1) + c, for n not equal to -1 |
Page 1 of 5. The full sheet, all 5 pages, opens free in the app.
What this Kinematics sheet covers
- Position, and the words that are not interchangeable
- The calculus this course actually needs
- The five derivatives and the one integral named
- Reading the three graphs of motion
- The equations for uniformly accelerated motion
- from a = dv/dt
- from v = dx/dt
- eliminating t
- distance in the nth second
- under gravity
- Vectors, and how they are written
- Adding vectors, three ways that agree
- Magnitude, direction and the two products
- resultant magnitude
- its direction
- scalar (dot) product
- vector (cross) product
- Projectile motion, one idea repeated twice
- Projectile results, for launch speed u at angle θ
- Uniform circular motion, in outline
- Relative velocity, which the graphs hide
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Physics chapter by chapter against your real exam dates and free hours, and when the plan reaches Kinematics the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.