Question

A particle moves in the *xy* plane. Its position vector
function of time is ?⃑ = (2?3 − 5?)?̂ + (6 − 7?4)?̂ where r is in
meters and t is in seconds.

a) In unit vector notation calculate the position vector at t =2
s.

b) Find the magnitude and direction of the position vector for part
a.

c) In unit vector notation calculate the velocity vector at t =2
s.

d) Find the magnitude and direction of the velocity vector for part
b.

e) In unit vector notation calculate the acceleration vector at t
=2 s.

f) Find the magnitude and direction of the acceleration vector for
part e.

Answer #1

Given ?⃑ = (2?^{3} − 5?)?̂ + (6 − 7?^{4})?̂

a) Position Vector at t=2s

b) Magnitude:

Direction :

c)

d) Magnitude =

Direction =

e) Similarly Accleration =

f) Magnitude =

Direction =

The acceleration of a particle moving only on a horizontal
xy plane is given by a→=3ti^+4tj^, where a→ is in meters
per second-squared and t is in seconds. At t = 0,
the position vector r→=(19.0m)i^+(44.0m)j^ locates the particle,
which then has the velocity vector v→=(5.40m/s)i^+(1.70m/s)j^. At
t = 4.10 s, what are (a) its position
vector in unit-vector notation and (b) the angle
between its direction of travel and the positive direction of the
x axis?

The vector position of a 3.80 g particle moving in the xy plane
varies in time according to
r (with arrow)1 = (3i + 3j)t + 2jt2 where t is in seconds and r
with arrow is in centimeters. At the same time, the vector position
of a 5.45 g particle varies as r (with arrow)2 = 3i − 2it2 −
6jt.
(a) Determine the vector position of the center of mass at
t = 2.90.
(b) Determine the linear...

A particle moves in the xy plane, starting from the origin at
t=0 with an initial velocity having an x-component of 6 m/s and y
component of 5 m/s. The particle experiences an acceleration in the
x-direction, given by ax=4t m/s2. Determine the acceleration vector
at any later time. Determine the total velocity vector at any later
time Calculate the velocity and speed of the particle at t=5.0 s,
and the angle the velocity vector makes with the x-axis. Determine...

The acceleration of a particle moving only on a horizontal xy
plane is given by ModifyingAbove a With right-arrow equals 4t
ModifyingAbove i With caret plus 5t ModifyingAbove j With caret,
where ModifyingAbove a With right-arrow is in meters per
second-squared and t is in seconds. At t = 0, the position vector
ModifyingAbove r With right-arrow equals left-parenthesis
24.0mright-parenthesis ModifyingAbove i With caret plus
left-parenthesis 49.0mright-parenthesis ModifyingAbove j With caret
locates the particle, which then has the velocity vector...

A particle starts from the origin with velocity 5 ?̂m/s at t = 0
and moves in the xy plane with a varying acceleration given by ?⃗ =
(2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and t is
in seconds. i) Determine the VELOCITY and the POSITION of the
particle as a function of time.

A
particle of mass m=0.2kg moves in the xy plane subject to a force
such as that its position as a function of time is given by the
vector r(t)= (3.0m/s2)t*2i+[12.0m-(2.0m/s*3)t*3]j
what is the magnitude of the torque on the particle about the
origin at the moment when the particle reaches the x axis?

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)....

A) A particle starts from the origin with velocity 5 ?̂m/s at t
= 0 and moves in the xy plane with a varying acceleration given by
?⃗ = (2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and
t is in seconds.
i) Determine the velocity of the particle as a function of
time.
ii) Determine the position of the particle as a function of
time.
(Explanation please )

1. The position of a bird in the xy-plane is given by ?⃗ =
(3.0?−∝ ?)?̂+ ?? 2 ?̂where ∝= 1.6 ?/? and ? = 0.8 ?/? 2 . a) What
are Vx(t) and Vy(t), x and y components of the velocity of the bird
as a function of time? b) What is the bird’s net velocity at 3.0 s
(magnitude and direction)? c) What are ax(t) and ay(t), x and y
components of the acceleration of the bird as...

Suppose that the position vector for a particle is given as a
function of time by vector r (t) = x(t)î + y(t)ĵ, with x(t) = at +
b and y(t) = ct2 + d, where a = 1.90 m/s, b = 1.10 m, c = 0.128
m/s2, and d = 1.12 m.
(a) Calculate the average velocity during the time interval from
t = 2.05 s to t = 3.75 s. vector v = m/s
(b) Determine the velocity...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 11 minutes ago

asked 12 minutes ago

asked 17 minutes ago

asked 22 minutes ago

asked 25 minutes ago

asked 40 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago