A particle moves with acceleration function a(t) = 2x+3. Its
initial velocity is v(0) = 2...
A particle moves with acceleration function a(t) = 2x+3. Its
initial velocity is v(0) = 2 m/s and its initial displacement is
s(0) = 5 m. Find its position after t seconds.
A particle moves along a line with velocity function ?(?) = ?^2
− ?, where v is measured in meters per second. a. Find distance
traveled by the particle in time interval [0, 6] seconds. b. Find
the net displacement. 8. Estimate the area from -1 to 9 under the
graph of f(x) = 81 – x^2 using five approximating rectangles and
midpoints as sample points.
A particle moves in the xy plane with constant acceleration. At
t = 0 the particle is at vector r1 = (3.6 m)i + (2.8 m)j, with
velocity vector v1. At t = 3 s, the particle has moved to vector r2
= (11 m)i − (1.8 m)j and its velocity has changed to vector v2 =
(4.6 m/s)i − (6.7 m/s)j. (a) Find vector v1. vector v1 = m/s
(b) What is the acceleration of the particle? vector a...
A particle moves in the xy plane with constant
acceleration. At t = 0 the particle is at r1 =
(4.0 m) + (3.0 m), with velocity 1. At t = 3 s,
the particle has moved to r2 = (9 m) − (2.0 m) and its
velocity has changed to v2 = (5.0 m/s) − (6.0 m/s).
i. Find 1 = m/s
ii. What is the acceleration of the particle?
iii. What is the velocity of the particle as...
. A particle is moving so that its velocity is v(t) = 3t 2 − 30t
+ 48 meters/min, where t is time in minutes.
a. Find the displacement (change in position) of the particle in
the first 12 minutes. Give units.
b. Find the total distance traveled by the particle in the first
12 minutes. Give units.
Find the velocity, acceleration, and speed of a particle with
the given position function.
r(t) =
9 cos(t), 8 sin(t)
v(t)
=
a(t)
=
|v(t)|
=
Sketch the path of the particle and draw the velocity and
acceleration vectors for
t =
π
3
.
Suppose that a particle has the following acceleration vector
and initial velocity and position vectors.
a(t) = 7 i +
9t k,
v(0) = 4 i
−
j, r(0)
= j + 5 k
(a)
Find the velocity of the particle at time t.
(b)
Find the position of the particle at time
t.
Particle A moves along an axis in the laboratory with velocity V
= 0.3c. Particle b moves with velocity of V = .9c along the
direction of motion of particle A.
What kinetic energy does the particle b measure for the particle
A?
The velocity function of a particle moving along a line is given
by the equation v(t) = t2 - 2t -3. The particle has
initial position s(0) = 4.
a. Find the displacement function
b. Find the displacement traveled between t = 2 and t = 4
c. Find when the particle is moving forwards and when it moves
backwards
d. Find the total distance traveled between t = 2 and t = 4
e. Find the acceleration function, and...
The velocity function for a particle moving along a straight
line is given by v(t) = 2 − 0.3t for 0 ≤ t ≤ 10, where t is in
seconds and v in meters/second. The particle starts at the
origin.
(a) Find the position and acceleration functions for this
particle.
(b) After ten seconds, how far is the particle from its starting
point?
(c) What is the total distance travelled by the particle in the
interval [0, 10]?