Question
In: Math
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.
Solutions
milcah answered 2 years agoRelated Solutions
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 displacement (in centimeters) of a particle moving back and forth along a straight line is...
The displacement (in centimeters) of a particle moving back and
forth along a straight line is given by the equation of motion
s = 3 sin(πt) + 4
cos(πt), where t is measured in
seconds. (Round your answers to two decimal places.)
(a) Find the average velocity during each time period.
(i) [1, 2]
_______cm/s
(ii) [1, 1.1]
_______ cm/s
(iii) [1, 1.01]
______ cm/s
(iv) [1, 1.001]
_______cm/s
B) Estimate the instantaneous velocity of the particle when
t=1.
1. The position of a particle moving in a straight line during a 5–second trip is...
1. The position of a particle moving in a straight line during a
5–second trip is s(t) =
2t2 − 2t + 2 cm.
Find a time t at which the instantaneous velocity is equal
to the average velocity for the entire trip beginning at
t = 0.
2. a) A particle moving along a line has position
s(t) =
t4 − 34t2
m at time t seconds. At which non negative times does the
particle pass through the origin?...
The position of a particle moving along the x axis is given in centimeters by x...
The position of a particle moving along the x axis is
given in centimeters by x = 9.72 + 1.85
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 instantaneous
velocity when the particle is...
An object is moving along a straight line, and the uncertainty in its position is 2.20...
An object is moving along a straight line, and the uncertainty
in its position is 2.20 m. (a) Find the minimum uncertainty in the
momentum of the object. Find the minimum uncertainty in the
object's velocity, assuming that the object is (b) a golf ball
(mass = 0.0450 kg) and (c) an electron.
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 displacement (in meters) of a particle moving in a straight line is given by s...
The displacement (in meters) of a particle moving in a straight
line is given by s = t^2 - 4t + 16, where t is measured in
seconds.
(a) Find the average velocity over each time interval.
(i) [3, 4]
(ii) [3.5, 4]
(iii) [4, 5]
(iv) [4, 4.5]
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 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."
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...
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