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3 days ago

An object is moving in the plane according to these parametric equations:

Physics

2 answers:

kicyunya [1K]3 days ago

8 0

Answer:

.a vx = -3π

b.vy = 0

c.c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]

d.m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]

e. t = -1.0

f.f. t = -0.35

g.vx = π - 4πsin (4π(0.124) + π/2)

h.vmax=4π cos (4π(0.045) + π/2)

i.s(t) = [x(t)^2 + y(t)^2]^(1/2)

s'(t) = d [x(t)^2 + y(t)^2]^(1/2) / dt

Explanation:

x(t) = πt + cos(4πt + π/2)

Finding the horizontal distance's derivative with respect to time t yields the horizontal velocity

The change in position over a change in time represents velocity

vx = dx/dt = π - 4πsin (4πt + π/2)

vx = π - 4π sin (0 + π/2)

when t = 0, substituting the value of t into the previous equation

vx = π - 4π (1)

vx = -3π

y(t) = sin(4πt + π/2)

finding the derivative with respect to t

dy/dt=4π cos (4πt + π/2)

π/2=90

when t=0

b. vy=dy/dt = 4π cos (4πt + π/2)

vy = 0

c. the slope of the tangent line

y(t)/x(t)

c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]

d. at t=1/6, substitute into the result found in c

m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]

e. t = -1.0

f. t = -0.35

g. Find t

vx = π - 4πsin (4πt + π/2) = 0

at the peak speed = 0

(4πt + π/2)=0.0043

t=-π/2+0.0043/(4π)

t=-0.124

vx = π - 4πsin (4π(0.124) + π/2)

h. Find t

vy = 4π cos (4πt + π/2) = 0

(4πt + π/2=1

t=0.57/4π

t=0.045

vmax=4π cos (4π(0.045) + π/2)

i. the resultant displacement

s(t) = [x(t)^2 + y(t)^2]^(1/2)

h. s'(t) = d [x(t)^2 + y(t)^2]^(1/2) / dt

s'(t)=

k and l. Solve for the time values

d [x(t)^2 + y(t)^2]^(1/2) / dt = 0

And substitute to find the maximum and minimum velocities.

Maru [1K]3 days ago

5 0

A. The horizontal component of velocity is
vx = dx/dt = π - 4πsin(4πt + π/2)
vx = π - 4πsin(0 + π/2)
vx = π - 4π(1)
vx = -3π

b. vy = 4πcos(4πt + π/2)
vy = 0

c. m = sin(4πt + π/2) / [πt + cos(4πt + π/2)]

d. m = sin(4π/6 + π/2) / [π/6 + cos(4π/6 + π/2)]

e. t = -1.0

f. t = -0.35

g. To find t, set
vx = π - 4πsin(4πt + π/2) = 0
Then use this to calculate vxmax

h. To determine t, set
vy = 4πcos(4πt + π/2) = 0
Then use this to find vymax

i. s(t) = [x(t)^2 + y(t)^2]^(1/2)

h. s'(t) = d[x(t)^2 + y(t)^2]^(1/2) / dt

k and l. Determine the values for t
d[x(t)^2 + y(t)^2]^(1/2) / dt = 0
And substitute to find both the maximum and minimum speeds.

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The flux across the cube's surface is $2.314\ Nm^{2}/C$ .

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According to the details provided:

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Now,

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where

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The volume charge density for this scenario is described by:

$\rho_{v} = \frac{Total\ charge, q}{Volume of cube, V}$

Cube volume, $V = a^{3}$ .

Thus,

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$q = 2.048\times 10^{-11}\ F = 20.48\ pF$ .

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Answer:

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