The position of a particle P on a line l is given by s(t) = t2 − 4t, where s(t) is in feet and t is in seconds.

Question

Determine the time intervals (in seconds) in which the particle moves in the positive direction and the negative direction. (Enter your answers using interval notation.)

Answer 1

s(t) = t^2 -4t

v(t)=s'(t) = 2t-4 = 0

t = 2 seconds when for an instant, it's not moving, changing direction

it's moving in a negative direction for t<2

it's moving in a positive direction for t>2

graphically the distance equation is an upward opening parabola

with vertex = (2,-4)

s=t^2-4t+4-4

=(t-2)^2 -4

to the left of the vertex, with t<2, the parabola is decreasing

to the right, with t>2, it's increasing