3.17 A particle is moving such that at any time t its position vector describes the parabola r(t) = (t – 1)i+(t-1)²j. (a) Write the path line in explicit form. (b) Sketch the path line that the particle travels over the time interval At = [0; 2]. (c) Determine expressions for the velocity v(t) and the acceleration a(t) at any time t. (d) Determine v(0), v(1), v(2), a(0), a(1), a(2) and draw them on a sketch.
3.17 A particle is moving such that at any time t its position vector describes the parabola r(t) = (t – 1)i+(t-1)²j. (a) Write the path line in explicit form. (b) Sketch the path line that the particle travels over the time interval At = [0; 2]. (c) Determine expressions for the velocity v(t) and the acceleration a(t) at any time t. (d) Determine v(0), v(1), v(2), a(0), a(1), a(2) and draw them on a sketch.
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![3.17 A particle is moving such that at any time t its position
vector describes the parabola r(t) = (t– 1)i+(t- 1)²j.
(a) Write the path line in explicit form.
(b) Sketch the path line that the particle travels over
the time interval At = [0; 2].
(c) Determine expressions for the velocity v(t) and
the acceleration a(t) at any time t.
(d) Determine v(0), v(1), v(2), a(0), a(1), a(2) and draw
them on a sketch.
r(t) = (t – 1)i + (t – 1)°j m
(a)
I = t - 1
» y = 1?
y = (t – 1)2
(b)
a(0)
a(2)
/v(2)
1
v(0)
a(1)
v(1)
Figuur / Figure 1: At = [0; 2] and Ar = [-1; 1]
(c) v(t) = i+2 (t – 1)j m/s
a(t) = 2j m/s?
(d) v(0) = i– 2j m/s; v(1) = i m/s; v(2) = i+ 2j m/s;
a(0) = a(1) = a(2) = 2j m/s²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e28af56-ebb8-4e2f-935d-2206564c45a0%2F5180ee54-afb4-4668-ab7b-af8fa5038c5c%2Fnihgvf_processed.png&w=3840&q=75)
Transcribed Image Text:3.17 A particle is moving such that at any time t its position
vector describes the parabola r(t) = (t– 1)i+(t- 1)²j.
(a) Write the path line in explicit form.
(b) Sketch the path line that the particle travels over
the time interval At = [0; 2].
(c) Determine expressions for the velocity v(t) and
the acceleration a(t) at any time t.
(d) Determine v(0), v(1), v(2), a(0), a(1), a(2) and draw
them on a sketch.
r(t) = (t – 1)i + (t – 1)°j m
(a)
I = t - 1
» y = 1?
y = (t – 1)2
(b)
a(0)
a(2)
/v(2)
1
v(0)
a(1)
v(1)
Figuur / Figure 1: At = [0; 2] and Ar = [-1; 1]
(c) v(t) = i+2 (t – 1)j m/s
a(t) = 2j m/s?
(d) v(0) = i– 2j m/s; v(1) = i m/s; v(2) = i+ 2j m/s;
a(0) = a(1) = a(2) = 2j m/s²
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