Question

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

Answer #1

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.

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

The
position of a particle in rectilinear motion is given by:
x(t) = (t^3 - 9t^2 + 24t + 5)ft. with t in seconds.
plot the position, velocity, and acceleration in the first 10
seconds

The position ? of a particle moving in space from (t=0 to 3.00
s) is given by ? = (6.00?^2− 2.00t^3 )i+ (3.00? − ?^2 )j+ (7.00?)?
in meters and t in seconds. Calculate (for t = 1.57 s): a. The
magnitude and direction of the velocity (relative to +x). b. The
magnitude and direction of the acceleration (relative to +y). c.
The angle between the velocity and the acceleration vector. d. The
average velocity from (t=0 to 3.00 s)....

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 position of a particle is given in cm by x = (2) cos 9?t,
where t is in seconds.
(a) Find the maximum speed.
0.565 m/s
(b) Find the maximum acceleration of the particle.
_______m/s2
(c) What is the first time that the particle is at x = 0 and
moving in the +x direction?
_______s

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

At time t, the vector ~r = 4t2i − (2t + 6t
2)ˆj gives the position of a 3 kg particle relative to
the origin of an xy coordinate system (~r is in meters and t is in
seconds). What is the torque (in Newton-meters) acting on the
particle relative to the origin?
ANSWER IS 48t, PLEASE EXPLAIN IN DETAIL HOW YOU GOT IT

1. (1’) The position function of a particle is given by s(t) =
3t2 − t3, t ≥ 0.
(a) When does the particle reach a velocity of 0 m/s? Explain the
significance of this value of t.
(b) When does the particle have acceleration 0 m/s2?
2. (1’) Evaluate the limit, if it exists.
lim |x|/x→0 x
3. (1’) Use implicit differentiation to find an equation of the
tangent line to the curve sin(x) + cos(y) = 1
at...

The position of a particle at time t ∈ R is given by
r(t) = (t 2 , 1/3 t(t 2 − 3)).
Specify for what value of t the velocity vector is vertical and
for what value of t the velocity vector is horizontal and at what
points in the plane this occurs.
b) Let z = ln(x + ln(y)). Determine all second order partial
derivatives to z.

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