Question

Find the distance traveled by a particle with position
(*x*, *y*) as *t* varies in the given time
interval.

x = 4 sin^{2}(t), y =
4 cos^{2}(t), 0 ≤ t ≤ 2π

What is the length of the curve?

Answer #1

The answer sheet has two pages.it is the first pagesecond /last page

Find the exact length of the curve. x = 8 + 9t2, y = 3 + 6t3, 0
≤ t ≤ 5
Find an equation of the tangent to the curve at the given point
by both eliminating the parameter and without eliminating the
parameter. x = 6 + ln(t), y = t2 + 1, (6, 2) y =
Find dy/dx. x = t 3 + t , y = 3 + t
Find the distance traveled by a particle...

If the acceleration of a particle is given by a(t)=2t-1 and the
velocity and position at time t=0 are v(0)=0 and S(0)=2.
1. Find a formula for the velocity v(t) at time t.
2. Find a formula for the position S(t) at time t.
3. Find the total distance traveled by the particle on the
interval [0,3].

A particle moves along a line with velocity v(t)=(3 -
t)(2+t), find the distance traveled during the time interval [0,
1].

A particle is moving with the given data. Find the position of
the particle. a(t) = 19 sin(t) + 2 cos(t), s(0) = 0, s(2π) = 16

A particle is moving with the given data. Find the position of
the particle. a(t) = 14 sin(t) + 3 cos(t), s(0) = 0, s(2π) = 18
s(t) =

A particle is moving with the given data. Find the position of
the particle.
a(t) = 18 sin(t) + 7 cos(t), s(0) =
0, s(2π) = 12
s(t)=

A particle is moving with the given data. Find the position of
the particle.
a(t) = 19 sin(t) + 2 cos(t), s(0) =
0, s(2π) = 12
s(t) =

A 3.60-kg particle moves along the x axis. Its position varies
with time according to x = t + 3.0t^3, where x is in meters and t
is in seconds. (a) Find the kinetic energy of the particle at any
time t. (Use the following as necessary: t.) K = (b) Find the
magnitude of the acceleration of the particle and the force acting
on it at time t. (Use the following as necessary: t.) a = F = (c)...

a particle is moving with the given data. find the position of
the particle.
a(t)= 10 sin t+3 cos t, s(0)=0, s(2π)=12

The equation x(t) = −bt2 +
ct3 gives the position of a particle traveling
along the x axis at any time. In this expression,
b = 4.00 m/s2, c = 4.80
m/s3, and x is in meters when t is
entered in seconds. For this particle, determine the following.
(Indicate the direction with the sign of your answer as
applicable.)
(a) displacement and distance traveled during the time interval
t = 0 to t = 3 s
displacement
distance
(b)...

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