The x and y coordinates of a particle in motion as functionsof
time t, are given by:
x=5t^2-5t+6 y=3t^3-3t^2-12t-4
At the instant the x-component of velocity is equal to
zero,the y component of the acceleration is closest to:
A. 12
B. -24
C. -15
D. -1.5
E. 3.0
particle is in simple harmonic motion along the x axis. The
amplitude of the motion is xm.
When it is at x = x1, its kinetic energy is K = 5 J and its
potential energy (measured with
U = 0 at x = 0) is U = 3 J. When it is at x = −1
2x1, the kinetic and potential energies are:
A. K = 5 J and U = 3J
B. K = 5 J and U...
The equation x(t) = A sin(ωt + φ) describes the
simple harmonic motion of a block attached to a spring with spring
constant k = 20 N/m. At t = 0 s, x = 0.5
m and the block is at rest.
a (5 points) After 0.5 s, the potential energy
stored in the spring first reaches zero and the velocity of the
block is in the negative x direction. What is the period of the
oscillation?
b (5 points)...
A particle executes simple harmonic motion, such that at a given
time, it is at ?A/3 moving in towards equilibrium.
0.7seconds later, it is at x=0.9A moving towards
equilibrium. Find the angular frequency of the particle, if it
passes through equilibrium once between the two occurrences.
Repeat the above, with the particle passing through equilibrium
5times between the two occurrences.
1.The position of a particle in rectilinear motion is given by s
(t) = 3sen (t) + t ^ 2 + 7. Find the speed of the particle when its
acceleration is zero.
2.Approximate the area bounded by the graph of y = -x ^ 2 + x +
2, the y-axis, the x-axis, and the line x = 2.
a) Using Reimmann sums with 4 subintervals and the extreme points
on the right.
b) Using Reimmann sums with 4...
The motion of a 16.1 lb. particle is given by:
r(ϴ) = (5sin 2ϴ) ft, with ϴ(t) = πt/4 rad,
and t in seconds.
Determine the magnitudes of the
particle’s position, velocity, acceleration, linear momentum, net
force, and T (K.E.) at t = 2 s.
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...
The position of a particle moving along an x axis is given by x
= 12.0t2 - 4.00t3, where x is in meters and t is in seconds.
Determine (a) the position, (b) the velocity, and (c) the
acceleration of the particle at t = 5.00 s. (d) What is the maximum
positive coordinate reached by the particle and (e) at what time is
it reached? (f) What is the maximum positive velocity reached by
the particle and (g) at...
The potential of a particle is given as V (x) = -Vδ (x), with V
being a positive number. Find the wave function and energy of the
bounded states of this particle.
The position of a particle moving along an x axis is
given by x = 16.0t2 -
6.00t3, where x is in meters and
t is in seconds. Determine (a) the
position, (b) the velocity, and
(c) the acceleration of the particle at t
= 3.00 s. (d) What is the maximum positive
coordinate reached by the particle and (e) at what
time is it reached? (f) What is the maximum
positive velocity reached by the particle and (g)
at...