Golf Ball Rolling Down an Incline

Question

As you watch this video, try to spot the hidden arithmetic and quadratic number series.

Answer

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.

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