The position of a particle moving along the x-axis is given by
x(t) = t^3 + 9t^2 − 21t with t is in [0, 2]. (a) Find the velocity
and acceleration of the particle.
(b) For what t-values is the velocity 0? (Enter your answers as
a comma-separated list.)
(c) When is the particle moving to the left (velocity is
negative)? (Enter your answer using interval notation.)
When is the particle moving to the right (velocity is positive)?
(Enter your...
The position vector F(t) of a moving particle at time t[s] is
given by F(t)= e^t sin(t)i-j+e^t cos(t)k a) Calculate the
acceleration a(t). b) Find the distance traveled by the particle at
time t = 3π/2, if the particle starts its motion at time t = π/2.
c) Find the unit tangent vector of this particle at time t = 3π/2.
d) Find the curvature of the path of this particle at time t =
3π/2.
2). A particle moving on the x-axis has a time-dependent
position (t) given by the equation x (t) = ct - bt^3. Where the
units of x are meters (m) and time t in seconds (s). (Hint: you
must get derivatives, you need graph paper)
(a) So that the position in x has units of meter which are the
units of the constants c and b?
If c = 5 and b = 1. From ti = 0s to tf...
Find the velocity, acceleration, and speed of a particle with
the given position function.
r(t) =
9 cos(t), 8 sin(t)
v(t)
=
a(t)
=
|v(t)|
=
Sketch the path of the particle and draw the velocity and
acceleration vectors for
t =
π
3
.
The position of a particle moving along a line (measured in
meters) is s(t) where t is measured in seconds. Answer all parts,
include units in your answers.
s(t)=2t^3 +6t^2 −48t+7 −10<t<10
(a) Find the velocity function.
(b) Find all times at which the particle is at rest.
(c) On what interval is the particle moving to the right?
(d) Is the particle slowing down or speeding up at t = −1
seconds?
A particle is moving according to the given data
v(t)=t^2 - sqrt(t), x(0) = 0, 0 ≤ t ≤ 4.
• Find x(t), the position of the particle at time t.
• For what values of t is the particle moving to the left? To the
right?
• Find the displacement of the particle.
• Find the total distance covered by the particle.
The position of a particle moving along the x axis is
given in centimeters by x = 9.72 + 1.85
t3, where t is in seconds. Calculate
(a) the average velocity during the time interval
t = 2.00 s to t = 3.00 s; (b)
the instantaneous velocity at t = 2.00 s;
(c) the instantaneous velocity at t =
3.00 s; (d) the instantaneous velocity at
t = 2.50 s; and (e) the instantaneous
velocity when the particle is...