The velocity of a subatomic particle moving through space can be modeled by

Question

v(t)=0.1t^2 −2t +0.2

for t≥0 where t is time in seconds and v is velocity in m/s.
Find the following:

a) (a) The time(s) t at which the particle is not moving:
......... and .........

b)The interval(s) over which the particle is moving forward: (Remember to write union as U and infinite as INF) ..................

c)The interval(s) over which the particle is moving backwards: (Remember to write union as U and infinite as INF) ..................

Thanks!

Answer 1

a) v(t)=0.1t^2 −2t +0.2 for t>=0
v = 0
t^2 - 20 t + 2 = 0
t = [ 20 +/- sqrt( 400 - 8 ) ] / 2
t = 10 +/- 0.5(sqrt 392)
t = 10 +/- 9.90
t = 20 or 0.1
it is negative between those points, when t -->inf +0.1 t^2 wins