Question
In: Math
a particle moves aling a straight line and its position at time t is given by...
a
particle moves aling a straight line and its position at time t is
given by s(t)= (t^3)-13.5t^2+54t where s is measured in feet and t
is seconds. consider t in the interval [0,infinity)
1) when is the particle moving in the positive direction? ( i
tried (0,3) U(6, infinity) but it didnt work)
2) what is the total distance the particle travels travels
between time 0 and time 7
3) when is the particle speeding up?
4) when is the particle slowing down?
Solutions
milcah answered 2 years agoRelated Solutions
An object moves along a straight line. The position as a function of time is given...
An object moves along a straight line. The position as a
function of time is given by the following
22 formula x(t)=5m+(2m/s)t–(0.6m/s)t^2. Please answer all of the
parts, I will give a good rating**** :)
How long after starting does it take the object to pass the
origin?
At what time is the object located 4 m from the origin?
Sketch the following graphs: x(t), v(t), a(t).
Find the object’s initial acceleration.
At what time will the object come to...
2. a. A particle moves in a straight line along with the ? − ???? its...
2. a. A particle moves in a straight line along with the ? −
???? its displacement is given by the equation ?(?) = 5? 3 − 8? 2 +
12? + 6,? ≥ 0, where ? is measured in seconds and s is measured in
meters. Find: i. The velocity function of the particle at time ?
(2marks) ii. The acceleration function of the particle at time t.
(2marks) iii. The acceleration after 5 seconds (1marks) b. Find the...
at time t=0, a particle is located at the point(4,8,7). it travels in a straight line...
at time t=0, a particle is located at the
point(4,8,7). it travels in a straight line to the point (7,1,6),
has speed 7 at (4,8,7) and constant acceleration 3i-7j-k. Find an
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Suppose a particle is moving right and left in a straight line. Its position, in centimeters,...
Suppose a particle is moving right and left in a straight
line. Its position, in centimeters, at time t seconds is given by
the function s(t) = −t3 + 12t2 − 21t. (For the purposes of this
problem, assume that t ≥ 0.)
(a) At what t-values is the particle stopped (that is, has a
velocity of zero)?
(b) Over what time interval(s) is the particle moving
left?
(c) Find the acceleration of the object when t = 4.
Suppose a particle is moving right and left in a straight line. Its position, in centimeters,...
Suppose a particle is moving right and left in a straight
line. Its position, in centimeters, at time t seconds is given by
the function s(t) = −t^3+ 12t^2 − 21t. (For the purposes of this
problem, assume that t ≥ 0.)
(a) At what t-values is the particle stopped (that is, has a
velocity of zero)?
(b) Over what time interval(s) is the particle moving
left?
c) Find the acceleration of the object when t = 4.
The velocity function for a particle moving along a straight line is given by v(t) =...
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]?
The position vector F(t) of a moving particle at time t[s] is given by F(t)= e^t...
The position vector F(t) of a moving particle at time t[s] is
given by F(t)= e^t sin(t)i-j+e^t cos(t)k a) Calculate the
acceleration a(t). b) Find the distance traveled by the particle at
time t = 3π/2, if the particle starts its motion at time t = π/2.
c) Find the unit tangent vector of this particle at time t = 3π/2.
d) Find the curvature of the path of this particle at time t =
3π/2.
A particle is moving with the given data. Find the position of the particle. a(t) =...
A particle is moving with the given data. Find the position of
the particle. a(t) = 11 sin(t) + 3 cos(t), s(0) = 0, s(2π) = 18
A particle is moving with the given data. Find the position of the particle. v(t) =...
A particle is moving with the given data. Find the position of
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A particle of mass M moves along a straight line with initial speed vi. A force...
A particle of mass M moves along a straight line with initial
speed vi. A force of magnitude Fpushes the particle a distance D
along the direction of its motion.
A) Find vf, the final speed of the particle after it has
traveled a distance D. Express the final speed in terms of vi, M,
F, and D.
B) By what multiplicative factor RK does the initial kinetic
energy increase, and by what multiplicative factor RW does the work
done...
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