The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds.

Question

The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds.

(a) Find the velocity and acceleration functions.

v(t): 3t^2 - 20t + 25

a(t): 6t - 20

(b) Over what interval(s) is the particle moving in the positive direction? Use inf to represent ∞, and U for the union of sets.

Interval:

(c) Over what interval(s) is the particle moving in the negative direction? Use inf to represent ∞, and U for the union of sets.

Interval:

(d) Over what interval(s) does the particle have positive acceleration? Use inf to represent ∞, and U for the union of sets.

Interval:

(e) Over what interval(s) does the particle have negative acceleration? Use inf to represent ∞, and U for the union of sets.

Interval:

(f) Over what interval is the particle speeding up? Slowing down? Use inf to represent ∞, and U for the union of sets.

Speeding up:

Slowing down:

Answer 1

-3t^2 -20t +25=0

3t^2 +20t -25 = 0

t =-20/6 +/-(1/6)sqr(400+300)

=-10/3 +/-10sqr7/6

= -10/3+5sqr7/3 (ignore the negative square root as t>0)

= (5sqr7-10)/3 = about 1.076 seconds

it's moving in a positive direction in the interval [0, 1.076)

in a negative direction in the interval (1.076, inf)

positive acceleration (3 1/3, inf)

negative acceleration [0, 3 1/3)

speed is the the absolute value of velocity

speed is a scalar, while velocity has magnitude and direction

speed is increasing when acceleration does not = 0

it's speeding up in the same intervals as when it's speeding down

[0, 3 1/3)U(3 1/3, inf)