Particle Motion: Video 1

Particle Motion

Increasing interval

↓

(5, 10) Do not include 5 or 10, since the first derivative is zero

Level 1

v(t) this is the first derivative Keep in mind that velocity is the average rate of positions

If the particle is moving, we have to use v(t)

t = 1 v(1) = 3(1)2 − 6(1) − 9

v(1)

v(1) = 3 − 6 − 9 v(1) = −12

velocity is negative and implies a left motion

so, equal the first derivative to zero 0 = 3t2 − 24t + 45 factor the trinomial 0 = 3(t2 − 8t + 15) 2

5

3

0 = t − 8t + 15 these are the zeros of the first derivative← t = 5 t = 3

∧ particle at rest