1Distance, Displacement & Average Speed
Average speed
Average velocity
Equal distances at speeds v₁ and v₂
Equal times at speeds v₁ and v₂
Distance ≥ |displacement|, so average speed ≥ |average velocity|. They are equal only for straight-line motion without turning back.
2Velocity, Acceleration & Variable Motion
Velocity from position
Acceleration from velocity
When v is given as a function of x
Going back: integrate
x(t) given → differentiate once for v, twice for a. a(t) given → integrate, and use the starting values to find the constant.
3Graphs of Motion
Slope of x–t graph
Slope of v–t graph
Area under v–t graphTake area below the time axis as negative; add magnitudes for distance.
Area under a–t graph
Uniform velocity: straight x–t line. Uniform acceleration: parabolic x–t curve and straight v–t line.
4Equations of Kinematics (constant acceleration)
First equation
Second equation
Third equation
Using average velocity
Distance in the nth second
Stopping distance (brakes)a is the size of the retardation.
Starting from rest, distances in successive equal seconds are in the ratio 1 : 3 : 5 : 7 …
5Motion Under Gravity (no air resistance)
Dropped from height h: time to fall
Dropped from height h: speed at ground
Thrown up with speed u: maximum height
Thrown up: time to top / total time
Taking upward as positive, use a = −g in the equations of motion. A body returns to its launch point with the same speed it was thrown with.
6Relative Velocity
Velocity of A relative to B
Same direction / opposite directions
Time for one train to cross another
Relative accelerationTwo bodies falling freely have zero relative acceleration.