The position vector r → of a particle moving in the xy plane is r → = 2 t i ^ + 2 sin [ ( π /4 rad/s) t ] j ^ , with r → in meters and t in seconds. (a) Calculate the x and y components of the particle’s position at t = 0, 1.0, 2.0, 3.0, and 4.0 s and sketch the particle’s path in the xy plane for the interval 0 ≤ t ≤ 4.0 s. (b) Calculate the components of the particle’s velocity at t = 1.0, 2.0, and 3.0 s. Show that the velocity is tangent to the path of the particle and in the direction the particle is moving at each time by drawing the velocity vectors on the plot of the particle’s path in part (a). (c) Calculate the components of the particle’s acceleration at t = 1.0, 2.0, and 3.0 s.
The position vector r → of a particle moving in the xy plane is r → = 2 t i ^ + 2 sin [ ( π /4 rad/s) t ] j ^ , with r → in meters and t in seconds. (a) Calculate the x and y components of the particle’s position at t = 0, 1.0, 2.0, 3.0, and 4.0 s and sketch the particle’s path in the xy plane for the interval 0 ≤ t ≤ 4.0 s. (b) Calculate the components of the particle’s velocity at t = 1.0, 2.0, and 3.0 s. Show that the velocity is tangent to the path of the particle and in the direction the particle is moving at each time by drawing the velocity vectors on the plot of the particle’s path in part (a). (c) Calculate the components of the particle’s acceleration at t = 1.0, 2.0, and 3.0 s.
The position vector
r
→
of a particle moving in the xy plane is
r
→
=
2
t
i
^
+
2
sin
[
(
π
/4 rad/s)
t
]
j
^
,
with
r
→
in meters and t in seconds. (a) Calculate the x and y components of the particle’s position at t = 0, 1.0, 2.0, 3.0, and 4.0 s and sketch the particle’s path in the xy plane for the interval 0 ≤ t ≤ 4.0 s. (b) Calculate the components of the particle’s velocity at t = 1.0, 2.0, and 3.0 s. Show that the velocity is tangent to the path of the particle and in the direction the particle is moving at each time by drawing the velocity vectors on the plot of the particle’s path in part (a). (c) Calculate the components of the particle’s acceleration at t = 1.0, 2.0, and 3.0 s.
Vectors u = −10i + 3j and v = −7i − 9j. What is u − v?
a
−17i − 6j
b
17i + 6j
c
3i − 12j
d
−3i + 12j
The position of a particle in space at time tis: r(t) = (sec(t)) * i + (tan t) * j + 4/3 tk. Write the particle's velocity at time t = (pi / 6) as the product of its speed and direction.
The equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors.
π
Then write the particle's velocity at t=
as a product of its speed and direction.
The velocity vector is v(t) = (i+j+ k.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.