Question

A
particle moves in a straight line and its position is given by
s(t)=t^3 - 6t^2-36t +66, where s is measured in feet and t in
seconds. Find the intervals when the particle increases its
speed.

Answer #1

A particle is moving along a straight line, and its position is
defined by s = (t2 - 6t +6) m. At t=6 seconds, find the following :
a. the acceleration of the particle b. The average speed c. the
average velocity

The position of a particle is given by s = f(t) = t^3 − 6t^2 +
9t. The total distance travelled by the particle in the first 5
seconds is :
A. 4
B. 20
C. 28
D. None of the above
The maximum vertical distance between the line y=x+2 and the
parabola y=x^2 for −1 ≤ x ≤ 2 is
A. 9/4
B. 1/4
C. 3/4
D. None of the above

The function s(t) describes the position of a particle moving
along a coordinate line, where s is in feet and t is in
seconds.
s(t) = 3t2 - 6t +3
A) Find the anti-derivative of the velocity function and
acceleration function in order to determine the position function.
To find the constant after integration use the fact that
s(0)=1.
B) Find when the particle is speeding up and slowing down.
C) Find the total distance from time 0 to time...

The
equation of motioj of a partucle is given by s(t)= t^3 -6t^2 +9t
where s is in meters and t is in seconds.
a) Find when the particle is moving in the negatuve
direction
b) Find when the particle is accelerating in the positive
direction

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m
/ s and its initial displacement is s( 0 ) = 5 m. Find the position
of the particle at t = 1 seconds.

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is: v(0) = 4 m/
and its initial displacement is s(0) = 5 ms. Find the position of
the particle at t = 1 seconds.
10 m
5 m
11 m
4 m
2m

A particle of mass 10kg moves in a straight line such that the
force (in Newtons) acting on it at time (in seconds) is given by
90t4+70t3+30,
If at time t=0 its velocity,v (in ms-1), is given by
v(0)=9 , and its position x (in m) is given by x(0)=6 , what is the
position of the particle at time ?

The position of an object moving horizontally after t seconds is
given by the function s =12t-t^3 , for t > 0, where s is
measured in feet, with s g> 0 corresponding to positions right
of the origin.
a. When is the object stationary, moving to the right, and
moving to the left?
b. Determine the velocity and acceleration of the object at
t=4.
c. Determine the acceleration of the object when its velocity is
zero.
d. On what...

In a 2 sec lab experiment a particle moves in a straight line
while its acceleration is manipulated by a force field. The
resulting acceleration function (in m/S^2<) is a multi part
function whose expression and graph are shown below.
A(t)={60(1-t) 0<(or equal to)t<1
{60(t-2) 1<(or equal to)t<2
Assume the particle begins at rest at t=0 seconds
A) compute the expression in terms of t for the velocity of the
particle from t=0 to t=1 seconds
B) compute the expression...

The position (in meters) of an object moving in a straight
line
s(t)=√ 3t+1 −2t^2+1
where t is measured in seconds.
(a) Find the average velocity on [0,1].
(b) Find the instantaneous velocity at t=1.
(c) Find the acceleration at t=1.

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