I asked this before but I don't understand part C. Could you explain it in easier terms?
The velocity of a subatomic particle moving through space can be modeled by
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!
I know A is The time(s) t at which the particle is not moving: 0.10 and 19.90
I know B is [0, 0.10) U(19.90, INF)
But:
I thought C would be (-0.10, 19.90) but it says wrong..
Thank you
The equation is only applicable at positive t.
-0.10 is not allowed
0.10 < t < 19.90 is when it is in reverse
Anonymous, how would I enter that in the boxes....see above image
thanks
To find the intervals over which the particle is moving backwards, we need to identify the values of time (t) when the velocity (v) is negative. In other words, we are looking for the time intervals where the particle's velocity is in the opposite direction.
Step 1: Set v(t) = 0 and solve for t to find the values where the particle changes direction.
0.1t^2 - 2t + 0.2 = 0
Step 2: Use the quadratic formula to solve for t:
t = (-(-2) ± √((-2)^2 - 4(0.1)(0.2))) / (2(0.1))
Simplifying:
t = (2 ± √(4 - 0.08)) / 0.2
t = (2 ± √(3.92)) / 0.2
t = (2 ± √3.92) / 0.2
t ≈ (2 ± 1.98) / 0.2
t ≈ 9.9 or 10.1
Step 3: Analyze the intervals:
The particle changes direction at t ≈ 9.9 and t ≈ 10.1. This means that the interval where the particle is moving backwards is between these two points. However, since we already know that the particle is not moving at t = 0.10 and t = 19.90 (from part A), we need to exclude those points from the interval.
The interval over which the particle is moving backwards is (0.10, 9.9) U (10.1, 19.90), which means it includes all the values of t between 0.10 and 9.9, as well as the values between 10.1 and 19.90, excluding the endpoints themselves.
Therefore, the correct answer for part C is:
The interval(s) over which the particle is moving backwards: (0.10, 9.9) U (10.1, 19.90)