exercise:25a3f1d194: Difference between revisions
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where it will be assumed that the unit of | where it will be assumed that the unit of | ||
distance in the plane is <math>1</math> foot. | distance in the plane is <math>1</math> foot. | ||
<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li> | ||
Identify and draw the curve which the particle traces | Identify and draw the curve which the particle traces | ||
out during its interval of motion.</li> | out during its interval of motion.</li> | ||
| Line 51: | Line 51: | ||
<math>t=0</math>, <math>t=1</math>, and <math>t=2</math>. | <math>t=0</math>, <math>t=1</math>, and <math>t=2</math>. | ||
Show these positions and draw the velocity | Show these positions and draw the velocity | ||
vectors in the figure in part | vectors in the figure in part (a).</li> | ||
<li>Compute the acceleration <math>\vec a(t)</math>. | <li>Compute the acceleration <math>\vec a(t)</math>. | ||
Find the times and corresponding positions | Find the times and corresponding positions | ||
(if any) when the acceleration and velocity vectors | (if any) when the acceleration and velocity vectors | ||
are perpendicular to each other.</li> | are perpendicular to each other.</li> | ||
<li> | <li> | ||
Write a definite integral equal to the distance (in feet) | Write a definite integral equal to the distance (in feet) | ||
which the particle moves during the interval | which the particle moves during the interval | ||
from <math>t=0</math> to <math>t=2</math> seconds.</li> | from <math>t=0</math> to <math>t=2</math> seconds.</li> | ||
<li>Evaluate the integral in | <li>Evaluate the integral in (d).</li> | ||
</ul> | </ul> | ||
Latest revision as of 23:56, 25 November 2024
[math]
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[/math]
A particle moves in the plane during the time interval from [math]t=0[/math] to [math]t=2[/math] seconds. Its position at any time during this interval is given by the parametrization
[[math]]
P(t) = (t,t^2-t)
,
[[/math]]
where it will be assumed that the unit of distance in the plane is [math]1[/math] foot.
- Identify and draw the curve which the particle traces out during its interval of motion.
- Compute the velocity vector [math]\vec v(t)[/math]. Find the position, velocity, and speed at [math]t=0[/math], [math]t=1[/math], and [math]t=2[/math]. Show these positions and draw the velocity vectors in the figure in part (a).
- Compute the acceleration [math]\vec a(t)[/math]. Find the times and corresponding positions (if any) when the acceleration and velocity vectors are perpendicular to each other.
- Write a definite integral equal to the distance (in feet) which the particle moves during the interval from [math]t=0[/math] to [math]t=2[/math] seconds.
- Evaluate the integral in (d).