meramera50
07.01.2020 •
Physics
The function
s
(
t
)
describes the motion of a particle along a line:
s
(
t
)
=
18
t
−
t
2
.
a) find the velocity function
v
(
t
)
of the particle at any time
t
≥
0.
b) identify the time interval in which the particle is moving in a positive direction.
c) identify the time interval in which the particle is moving in a negative direction.
d) identify the time at which the particle changes direction.
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Ответ:
a)
b)
c)
d)
Explanation:
We have the following parts:
(a) find the velocity function of the particle at any time t ≥0 )
For this case w ejust need to take the derivate of s(t) and we got:
(b) identify the time interval(s) in which the particle is moving in a positive direction
The partcile is moving in the positive direction when the velocity is higher than 0. We have a quadratic equation for the velocity so we can solve for the t intercepts like this:
For this case
And if we replace we got:
And now we can see on which intervals we have the velocity positive or negative:
So the is positive between
(c) identify the time interval(s) in which the particle is moving in a negative direction
From the before part we see that the velocity is negative just on this interval:
(d) identify the time(s) at which the particle changes direction. s(t) = t³ - 5t²+4t
The points where the particle changes direction are given by the critical point because are the points where the derivate is 0 and we have the change of direction and on this case are:
Ответ:
Madeline is near death, while Roderick's sensitivity (or possible hypochondria) prevents him from leaving the house, ensuring the end of their line.
Explanation:
So it affect the plot maybe making the plot unfinished or not being able to pay the workers so it's important to the development of the plot.