(a) By eliminating the parameter, sketch the trajectory over the time interval 0 ≤ t ≤ 5 of the particle whose parametric equations of motion are x = t − 1 , y = t + 1 (b) Indicate the direction of motion on your sketch. (c) Make a table of x - and y -coordinates of the particle at times t = 0 , 1 , 2 , 3 , 4 , 5. (d) Mark the position of the particle on the curve at the times in part (c), and label those positions with the values of t .
(a) By eliminating the parameter, sketch the trajectory over the time interval 0 ≤ t ≤ 5 of the particle whose parametric equations of motion are x = t − 1 , y = t + 1 (b) Indicate the direction of motion on your sketch. (c) Make a table of x - and y -coordinates of the particle at times t = 0 , 1 , 2 , 3 , 4 , 5. (d) Mark the position of the particle on the curve at the times in part (c), and label those positions with the values of t .
(a) By eliminating the parameter, sketch the trajectory over the time interval
0
≤
t
≤
5
of the particle whose parametric equations of motion are
x
=
t
−
1
,
y
=
t
+
1
(b) Indicate the direction of motion on your sketch.
(c) Make a table of x- and y-coordinates of the particle at times
t
=
0
,
1
,
2
,
3
,
4
,
5.
(d) Mark the position of the particle on the curve at the times in part (c), and label those positions with the values of t.
Find parametric equations and a parameter interval for the motion of a particle starting at the point (2, 0) and tracing the top half of the circle x2 + y2 = 4 four times.
find the parametric equations for the line segment from (-2,5) to (7,-1) your equation for x should not be x=t. define your interval for the parameter t.
Find the points (x, y) on the curve with the parametric equations
(x3Dt3- 4t
at
ly=t +2
which the tangent lines are vertical or horizontal.
University Calculus: Early Transcendentals (3rd Edition)
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