As you watch this video, try to spot the hidden arithmetic and quadratic number series.
A ball rolling down an incline has a constant acceleration of gsinθ.
Because the acceleration is constant,
- the velocity increases linearly with time (v=at), and
- the displacement quadratically with time (s=½at2)
In addition, because the motion starts from v=0 at t=0, the (a) velocity, (b) distance travelled per unit time, and (c) total accumulative distance travelled, all form very nice number series.
(a) Velocity : 0, 1, 2, 3, 4,
(b) Distance: 1, 3, 5, 7
(c) Total distance: 1, 4, 9, 16
The v-t graph below explains why.