Question

A particle's position is given by x = 7.00 - 15.00t + 3t2, in which x is in meters and t is in seconds. (a) What is its velocity at t = 1 s? (b) Is it moving in the positive or negative direction of x just then? (c) What is its speed just then? (d) Is the speed increasing or decreasing just then? (Try answering the next two questions without further calculation.) (e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer "0". (f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer "0".

Answer #1

A particle's position is given by x = 12.0 - 9.00t + 3t2, in
which x is in meters and t is in seconds. (a) What is its velocity
at t = 1 s? (b) Is it moving in the positive or negative direction
of x just then? (c) What is its speed just then? (d) Is the speed
increasing or decreasing just then? (Try answering the next two
questions without further calculation.) (e) Is there ever an
instant when...

1) The position of a particle moving along x direction is given
by: x=8t-3t2.What is the velocity of the particle at t=2
s and what is the acceleration?
2) A roller coaster car starts from rest and descends
h1= 40 m. The car has a mass of 75 kg. What is the speed
at 20m while going down the hill?

The position of a particle in cm is given by x = (9)
cos 3πt, where t is in seconds.
(a) What is the frequency?
Hz
(b) What is the period?
s
(c) What is the amplitude of the particle's motion?
cm
(d) What is the first time after t = 0 that the particle
is at its equilibrium position?
s
In what direction is it moving at that time?
* in the positive direction
* in the negative direction

1. (1’) The position function of a particle is given by s(t) =
3t2 − t3, t ≥ 0.
(a) When does the particle reach a velocity of 0 m/s? Explain the
significance of this value of t.
(b) When does the particle have acceleration 0 m/s2?
2. (1’) Evaluate the limit, if it exists.
lim |x|/x→0 x
3. (1’) Use implicit differentiation to find an equation of the
tangent line to the curve sin(x) + cos(y) = 1
at...

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)....

please do 1,2 and 3 thanks
1.The position of a particle moving along the x axis is
given in centimeters by x = 9.12 + 1.75
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...

1)A particle moves along the x axis. Its position is
given by the equation
x = 1.8 + 2.5t − 3.9t2
with x in meters and t in seconds.
(a) Determine its position when it changes direction.
(b) Determine its velocity when it returns to the position it had
at t = 0? (Indicate the direction of the velocity with the
sign of your answer.)
2)The height of a helicopter above the ground is given by
h = 3.10t3, where...

The equation x(t) = −bt2 +
ct3 gives the position of a particle traveling
along the x axis at any time. In this expression,
b = 4.00 m/s2, c = 4.80
m/s3, and x is in meters when t is
entered in seconds. For this particle, determine the following.
(Indicate the direction with the sign of your answer as
applicable.)
(a) displacement and distance traveled during the time interval
t = 0 to t = 3 s
displacement
distance
(b)...

The velocity function of a particle is given by v(t) = 3t2 – 24t
+ 36.
a) Find the equation for a(t), the acceleration.
b) If s(1) = 50, find the displacement function s(t).
c) When will the velocity be zero?
d) Find the distance the particle travels on [0, 4].

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

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