Question

The
equation of motioj of a partucle is given by s(t)= t^3 -6t^2 +9t
where s is in meters and t is in seconds.

a) Find when the particle is moving in the negatuve
direction

b) Find when the particle is accelerating in the positive
direction

Answer #1

) A particle is moving according to the velocity equation v(t) =
9t^2-8t-2 . The equation uses units of meters and seconds
appropriately. At t = 1 s the particle is located at x = 2 m. (a)
What is the particle's position at t = 2 s? (b) What is the
particle's acceleration at t = 1 s? (c) What is the particle's
average velocity from t = 2 s to t = 3 s?

The position of a particle is given by s = f(t) = t^3 − 6t^2 +
9t. The total distance travelled by the particle in the first 5
seconds is :
A. 4
B. 20
C. 28
D. None of the above
The maximum vertical distance between the line y=x+2 and the
parabola y=x^2 for −1 ≤ x ≤ 2 is
A. 9/4
B. 1/4
C. 3/4
D. None of the above

A
particle moves in a straight line and its position is given by
s(t)=t^3 - 6t^2-36t +66, where s is measured in feet and t in
seconds. Find the intervals when the particle increases its
speed.

The
position of a particle in rectilinear motion is given by:
x(t) = (t^3 - 9t^2 + 24t + 5)ft. with t in seconds.
plot the position, velocity, and acceleration in the first 10
seconds

Given: v(t) = 6t - 6, on .
The velocity function (in meters per second) is given
for a particle moving along a line. Find the total (left and
right) distance traveled by the particle during the
given time interval from t = 0 to t = 5.

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

The velocity of a particle moving along a line is a function of
time given by v(t)=81/(t2+9t+18). Find the
distance
that the particle has traveled after t=9 seconds if it started at
t=0 seconds.

The function s(t) describes the position of a particle moving
along a coordinate line, where s is in feet and t is in
seconds.
s(t) = 3t2 - 6t +3
A) Find the anti-derivative of the velocity function and
acceleration function in order to determine the position function.
To find the constant after integration use the fact that
s(0)=1.
B) Find when the particle is speeding up and slowing down.
C) Find the total distance from time 0 to time...

A particle moves according to a law of motion s = f(t), t ≥ 0,
where t is measured in seconds and s in feet. f(t) = 0.02t4 −
0.08t3 (a) Find the velocity at time t. (b) What is the velocity
after 3 s? (c) When is the particle at rest? (Enter your answers as
a comma-separated list.) (d) When is the particle moving in a
positive direction? (Enter your answer using interval notation.)
(e) Find the total distance...

The position ? of a particle moving in space from (t=0 to 3.00
s) is given by ? = (6.00?^2− 2.00t^3 )i+ (3.00? − ?^2 )j+ (7.00?)?
in meters and t in seconds. Calculate (for t = 1.57 s): a. The
magnitude and direction of the velocity (relative to +x). b. The
magnitude and direction of the acceleration (relative to +y). c.
The angle between the velocity and the acceleration vector. d. The
average velocity from (t=0 to 3.00 s)....

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