2.57 • CALC The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s³)r³ – (10.0 m/s²)t² + (9.00 m/s)t. (a) Draw the x-t, v,-t, and a,-t graphs of this particle. (b) At what time(s) between t = 0 and t = 2.00 s is the particle instantaneously at rest? Does your numerical result agree with the v,-t graph in part (a)? (c) At each time calculated in part (b), is the acceleration of the particle positive or negative? Show that in each case the same answer is deduced from a,(1) and from the v,-t graph. (d) At what time(s) between 1 = 0 and t = 2.00 s is the velocity of the particle instantaneously not changing? Locate this point on the Vg-t and a,-t graphs of part (a). (e) What is the particle's greatest dis- tance from the origin (x = 0) between t = 0 and t = 2.00 s? (f) At what time(s) between t = 0 and t = 2.00 s is the particle speeding up at the greatest rate? At what time(s) between t = 0 and t = 2.00 s is the particle slowing down at the greatest rate? Locate these points on the v,-t and a,-t graphs of part (a).
2.57 • CALC The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s³)r³ – (10.0 m/s²)t² + (9.00 m/s)t. (a) Draw the x-t, v,-t, and a,-t graphs of this particle. (b) At what time(s) between t = 0 and t = 2.00 s is the particle instantaneously at rest? Does your numerical result agree with the v,-t graph in part (a)? (c) At each time calculated in part (b), is the acceleration of the particle positive or negative? Show that in each case the same answer is deduced from a,(1) and from the v,-t graph. (d) At what time(s) between 1 = 0 and t = 2.00 s is the velocity of the particle instantaneously not changing? Locate this point on the Vg-t and a,-t graphs of part (a). (e) What is the particle's greatest dis- tance from the origin (x = 0) between t = 0 and t = 2.00 s? (f) At what time(s) between t = 0 and t = 2.00 s is the particle speeding up at the greatest rate? At what time(s) between t = 0 and t = 2.00 s is the particle slowing down at the greatest rate? Locate these points on the v,-t and a,-t graphs of part (a).
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:2.57
CALC The position of a particle between t = 0 and
1 = 2.00 s is given by x(1) = (3.00 m/s³);³ – (10.0 m/s²)r² +
(9.00 m/s)t. (a) Draw the x-t, v,-t, and a,-t graphs of this particle.
(b) At what time(s) between t = 0 and t = 2.00 s is the particle
instantaneously at rest? Does your numerical result agree with
the v,-t graph in part (a)? (c) At each time calculated in part (b), is the
acceleration of the particle positive or negative? Show that in each
case the same answer is deduced from a,(t) and from the v,-t graph.
(d) At what time(s) between t = 0 and t = 2.00 s is the velocity of
the particle instantaneously not changing? Locate this point on the
vy-t and a,-t graphs of part (a). (e) What is the particle's greatest dis-
tance from the origin (x = 0) between t = 0 and t = 2.00 s? (f) At
what time(s) between 1 = 0 and 1 = 2.00 s is the particle speeding
up at the greatest rate? At what time(s) between t = 0 and
t = 2.00 s is the particle slowing down at the greatest rate? Locate
these points on the v-t and a,-t graphs of part (a).
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