Question

A particle is moving according to the given data a(t) = sin t + 3 cos t, x(0) = 0, v(0) = 2.

where a(t) represents the acceleration of the particle at time t. Find v(t), the velocity of the particle at time t, and x(t), the position of the particle at time t.

Answer #1

Consider a particle moving through space with velocity v(t) =
cos(t)i−sin(t)j + tk.
(i) Determine its acceleration vector.
(ii) Determine the position vector, supposing the
particle starts at position (3,−2,3) at time t = 0.

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)= 10 sin t+3 cos t, s(0)=0, s(2π)=12

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 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)=

The position of a particle is given in cm by x = (2) cos 9?t,
where t is in seconds.
(a) Find the maximum speed.
0.565 m/s
(b) Find the maximum acceleration of the particle.
_______m/s2
(c) What is the first time that the particle is at x = 0 and
moving in the +x direction?
_______s

A particle is moving with the given data. Find the position of
the particle. a(t) = 2t + 5, s(0) = 3, v(0) = −5
s(t) =

A particle is moving with the given data. Find the position of
the particle. a(t) = 2t + 7, s(0) = 3, v(0) = −5

The velocity of a particle moving along the x-axis
varies with time according to
v(t) = A +
Bt−1,
where
A = 7 m/s,
B = 0.33 m,
and
1.0 s ≤ t ≤ 8.0 s.
Determine the acceleration (in m/s2) and position (in
m) of the particle at
t = 2.6 s
and
t = 5.6 s.
Assume that
x(t = 1 s) = 0.
t = 2.6 s
acceleration m/s2 position m
?
t = 5.6 s
acceleration m/s2
position m ?

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