Question

A toy car, A, moves horizontally along the positive x- axis such
that its position at time t > 0 is given by

the function

s(t) = 7t^{3} – 6t^{2} + 3, where t is time in
seconds.

(c) A toy truck, B, moves vertically along the positive y- axis
such that its position at time t > 0 is given by

the function: g(t) = 5t + 2. For any time t, t > 0, the position
of toy car A, toy truck B and the origin form

a right triangle in the first quadrant. What is the rate of change
of the area of the triangle at time t = 2

seconds? Show all the calculations that lead to your answer.

Answer #1

mass of 2kg moves horizontally along x axis under the
action of a force in terms of time, given as following: F(t) = b
sin wt , where t time in seconds , b and w are constants
1) find the impulse during t1=0 to t2=2
if the mass starts motion from rest at x=0
(Show in integration IN DETAIL)
2) find its velocity as function of time
(IN DETAIL)
3) find its position as function of time
(IN DETAIL)

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...

A particle moves along the x axis. It is initially at the
position 0.150 m, moving with velocity 0.080 m/s and acceleration
-0.340 m/s2. Suppose it moves with constant acceleration for 5.60
s. (a) Find the position of the particle after this time. (b) Find
its velocity at the end of this time interval. Next, assume it
moves with simple harmonic motion for 5.60 s and x = 0 is its
equilibrium position. (Assume that the velocity and acceleration is...

A 4.60 kg particle moves along the x axis. Its position
varies with time according to x = t +
1.8t3, where x is in meters and
t is in seconds.
(a) Find the kinetic energy at any time t. (Accurately
round any coefficient to exactly two decimal places. Use t as
necessary
_______J
(b) Find the acceleration of the particle and the force acting
on it at time t. (Accurately round any coefficient to
exactly two decimal places. Use...

A proton moves along the x axis according to the equation x =
50t + 10t2, where x is in meters and t is in seconds.
For the time range, -8 s ≤ t ≤ 4s, answer the questions
below. Show all work and explain your answers.
a) Estimate the fathest distance this proton could move in the
negative direction of the x axis. What is the velocity at
the moment?
b) In this time range, find out when the...

A particle moves along the x axis. It is initially at the
position 0.150 m, moving with velocity 0.080 m/s and acceleration
-0.340 m/s2. Suppose it moves with constant acceleration for 5.60
s. (c) Find its position (d) Find its velocity at the end of this
time interval.

The position of a particle moving along the x axis is given in
meters by x = 3.0t2 – 1.0t3, where t is in
seconds. (a.) At what time does the particle reach its maximum
positive x position? (b.) What total length of path does the
particle cover in the first 4.0 sec? (c.) What is its displacement
during the first 4.0 sec? (d.) What is the particle’s speed at the
end of the first 4 sec? (e.) What is...

A particle moves along a circular path having a radius of 6 in.
such that its position as a function of time is given by
theta=(cos4t)rad where t is in seconds. Determine the magnitude of
the acceleration of the particle when theta = 30.

Two particles move along an x axis. The position of
particle 1 is given by x = 10.0t2 +
6.00t + 4.00 (in meters and seconds); the acceleration of
particle 2 is given by a = -9.00t (in meters per seconds
squared and seconds) and, at t = 0, its velocity is 24.0
m/s. When the velocities of the particles match, what is their
velocity?

A particle moving along the x axis in simple harmonic motion
starts from its equilibrium position, the maximum value, at t = 0,
moving to the right. The amplitude of the motion is 2.00 cm and the
frequency is 1.50 Hz. (a) Find an expression for the position of
the particle as a function of time. Determine (b) the maximum speed
of the particle and (c) the earliest time (t > 0) at which the
particle has this speed. Find...

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