Question

The position of a particle is given by x = 2cos πt, where x is in meters and t is in seconds. (a) Find the maximum speed and (b) maximum acceleration of the particle?

Answer #1

Comment the maximum speed of the particle was found to be 6.283 m/s.

The maximum acceleration of the particle was found to be 19.739 m/s^2

The position of a particle is given in cm by x = (2)
cos 6πt, where t is in seconds.
(a) Find the maximum speed.
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 position of a particle is given in cm by x = (9)
cos 5πt, where t is in seconds.
(a) Find the maximum speed.
.... 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 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 position of a particle moving along the x axis is given in
meters by x = 3.0t2 – 1.0t3, where t is in
seconds. (a.) At what time does the particle reach its maximum
positive x position? (b.) What total length of path does the
particle cover in the first 4.0 sec? (c.) What is its displacement
during the first 4.0 sec? (d.) What is the particle’s speed at the
end of the first 4 sec? (e.) What is...

The position of a particle moving with constant acceleration is
given by x(t) = 2t2 +
8t + 4 where x is in meters and t is in
seconds.
(a) Calculate the average velocity of this particle between
t = 6 seconds and t = 9 seconds.
(b) At what time during this interval is the average
velocity equal to the instantaneous velocity?

1) The position of a particle is given in cm by x = (4)
cos 3πt, where t is in seconds.
(a) Find the maximum speed.
m/s
(b) Find the maximum acceleration of the particle.
m/s2
2) An object of mass m is suspended from a vertical
spring of force constant 1692 N/m. When the object is pulled down
2.51 cm from equilibrium and released from rest, the object
oscillates at 5.10 Hz. Write expressions for the acceleration
ax...

The position of a particle moving with constant acceleration is
given by
x(t) = 4t2 + 3t +
4
where x is in meters and t is in seconds.
(a) Calculate the average velocity of this particle between
t = 2 seconds and t = 7 seconds.
(b) At what time during this interval is the average velocity equal
to the instantaneous velocity?
(c) How does this time compare to the average time for this
interval?
a. It is larger....

Two particles move along an x axis. The position of
particle 1 is given by x = 10.0t2 +
6.00t + 4.00 (in meters and seconds); the acceleration of
particle 2 is given by a = -9.00t (in meters per seconds
squared and seconds) and, at t = 0, its velocity is 24.0
m/s. When the velocities of the particles match, what is their
velocity?

the position of an object in one dimension is given by
X(t)=A+Bt+Ct^2, where x is in meters and t is in seconds. find the
velocity and acceleration at 3 seconds. what are the units for A,
B, and C?

PROBLEM 1
The position of a particle on the x axis is given by:
x = 5.00 – 8.00 t + 2.00 t
2
with t in seconds and x in meters.
a) Calculate the value of x the moment the particle momentarily
stops.
b) When t = 0.500 s, is the particle speeding up or slowing down?
Explain.
PROBLEM 2
A ball is kicked at an angle θ0 with the horizontal with an initial
speed of 20.0 m /...

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