Question
In: Math
The function s=−t^3+12t^2−48t , 0≤t≤5, gives the position of a body moving on a coordinate line,...
The function s=−t^3+12t^2−48t , 0≤t≤5, gives the position of a body moving on a coordinate line, with s in meters and t in seconds.
a. Find the body's displacement and average velocity for the given time interval.
b. Find the body's speed and acceleration at the endpoints of the interval.
c. When, if ever, during the interval does the body change direction?
Solutions
milcah answered 2 years agoRelated Solutions
The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function...
The function
sequals=?f(t)
gives the position of an object moving along the? s-axis as a
function of time t. Graph f together with the velocity function
?v(t)equals=StartFraction ds Over dt EndFractiondsdtequals=f
prime left parenthesis t right parenthesisf?(t)
and the acceleration function
?a(t)equals=StartFraction d squared s Over dt squared
EndFractiond2sdt2equals=f prime prime left parenthesis t right
parenthesisf??(t)?,
then complete parts? (a) through? (f).
sequals=112112tminus?16 t squared16t2?,
0less than or equals?tless than or equals?77
?(a heavy object fired straight up from? Earth's...
1) The position of an object moving along a straight line is s(t) = t^3 −...
1) The position of an object moving along a straight
line is s(t) = t^3 − 15t^2 + 72t feet after t seconds. Find the
object's velocity and acceleration after 9 seconds.
2) Given the function f (x ) =−3 x 2 + x − 8 ,
(a) Find the equation of the line tangent to f(x ) at the point (2,
−2) .
(b) Find the equation of the line normal to f(x ) at the point (2,
−2)...
The position of a particle moving along a line (measured in meters) is s(t) where t...
The position of a particle moving along a line (measured in
meters) is s(t) where t is measured in seconds. Answer all parts,
include units in your answers.
s(t)=2t^3 +6t^2 −48t+7 −10<t<10
(a) Find the velocity function.
(b) Find all times at which the particle is at rest.
(c) On what interval is the particle moving to the right?
(d) Is the particle slowing down or speeding up at t = −1
seconds?
The position function of an object moving along a straight line is given by the function...
The position function of an object moving along a
straight line is given by the function t3 - 15t2 -48t -10, where s
is in metres and t is in seconds and 0≤15≤t . [7A]
a) When is the velocity of the object greater than 21
m/s?
b) When is the speed of the object less than 21
m/s?
c) Illustrate the graphical representation for each of
the above."
a car moving with uniform acceleration haas x coordinate at 7 m at t= 0. if...
a car moving with uniform acceleration haas x coordinate at 7
m at t= 0. if x coordinate at a time 4.2 sec later is -3m and at
this coordinate, if it moves with a speed magnitude of 20m/s in
negative x direction. find car's avg velocity, initial velocity,
and acceleration.
s(t)= 5t + 3/t^2 be the position in feet of a particle after t seconds for t...
s(t)= 5t + 3/t^2 be the position in feet of a
particle after t seconds for t ≥ 1.
(a) Compute the average velocity from t = 1 to t = 3. Include
units in your answer
(b) Where is the velocity = 0?
(c) Show the accelaration for t ≥ 1 is positive.
(d) What are the units for the acceleration?
Find the Laplace transforms: F(s)=L{f(t)} of the function f(t)=(8−t)(u(t−2)−u(t−5)), for s≠0. F(s)=L{f(t)}=
Find the Laplace transforms:
F(s)=L{f(t)} of the function
f(t)=(8−t)(u(t−2)−u(t−5)),
for s≠0.
F(s)=L{f(t)}=
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 according to the given data v(t)=t^2 - sqrt(t), x(0) = 0, 0...
A particle is moving according to the given data
v(t)=t^2 - sqrt(t), x(0) = 0, 0 ≤ t ≤ 4.
• Find x(t), the position of the particle at time t.
• For what values of t is the particle moving to the left? To the
right?
• Find the displacement of the particle.
• Find the total distance covered by the particle.
The position of a particle moving along the x-axis is given by x(t) = t^3 +...
The position of a particle moving along the x-axis is given by
x(t) = t^3 + 9t^2 − 21t with t is in [0, 2]. (a) Find the velocity
and acceleration of the particle.
(b) For what t-values is the velocity 0? (Enter your answers as
a comma-separated list.)
(c) When is the particle moving to the left (velocity is
negative)? (Enter your answer using interval notation.)
When is the particle moving to the right (velocity is positive)?
(Enter your...
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