Question

A particle moves according to a law of motion

* s* =

where *t* is measured in seconds and *s* in
feet.

* f*(

(a) Find the velocity at time *t*.

* v*(

(b) What is the velocity after 4 s?

* v*(4) = ft/s

(c) When is the particle at rest?

t = s (smaller value) |

t = s (larger value) |

(d) When is the particle moving in the positive direction? (Enter
your answer in interval notation.)

*t*

(e) Find the total distance traveled during the first 6 s.

ft

(f) Find the acceleration at time *t*.

* a*(

Find the acceleration after 4 s.

* a*(4) = ft/s

(g) Graph the position, velocity, and acceleration functions for
the first 6 s.

(h) When, for

0 ≤ * t* < ∞,

is the particle speeding up? (Enter your answer in interval notation.)

When, for

0 ≤ * t* < ∞,

is it slowing down? (Enter your answer in interval notation.)

Answer #1

A particle moves according to a law of motion
s = f(t),
t ≥ 0,
where t is measured in seconds and s in feet.
(If an answer does not exist, enter DNE.)
f(t) = t3 − 8t2 + 23t
(a) Find the velocity at time t.
v(t) = ft/s
(b) What is the velocity after 1 second?
v(1) = ft/s
(c) When is the particle at rest?
(d) When is the particle moving in the positive direction? (Enter
your...

A particle moves according to a law of motion
s = f(t),
t ≥ 0,
where t is measured in seconds and s in
feet.
f(t) =
t3 − 15t2
+ 72t
(a) Find the velocity at time t.
v(t) =
(b) What is the velocity after 5 s?
v(5) =
(c) When is the particle at rest?
t = s (smaller value)
t = s (larger value)
When is the particle moving in the positive direction? (Enter
your answer in interval...

A particle moves according to a law of motion
s = f(t),
t ≥ 0,
where t is measured in seconds and s in
feet.
f(t) =
t3 − 15t2
+ 72t
(a) Find the velocity at time t.
v(t) =
(b) What is the velocity after 5 s?
v(5) =
(c) When is the particle at rest?
t = s (smaller value)
t = s (larger value)
When is the particle moving in the positive direction? (Enter
your answer in interval...

A particle moves according to a law of motion s = f(t), t ≥ 0,
where t is measured in seconds and s in feet. (If an answer does
not exist, enter DNE.) f(t) = t3 − 8t2 + 27t (a) Find the velocity
at time t. v(t) = ft/s (b) What is the velocity after 1 second?
v(1) = ft/s (c) When is the particle at rest? (d) When is the
particle moving in the positive direction? (Enter your...

A particle moves according to a law of motion s = f(t), t ≥ 0,
where t is measured in seconds and s in feet. (If an answer does
not exist, enter DNE.) f(t) = t3 − 8t2 + 26t
A. Find the acceleration at time t and after 1 second.
a(t) = ft/s2
a(1) = ft/s2
B. When is the particle speeding up? (Enter your answer using
interval notation.)
c. When is it slowing down? (Enter your answer using...

A particle moves according to a law of motion s = f(t), t ≥ 0,
where t is measured in seconds and s in feet. f(t) = 0.02t4 −
0.08t3 (a) Find the velocity at time t. (b) What is the velocity
after 3 s? (c) When is the particle at rest? (Enter your answers as
a comma-separated list.) (d) When is the particle moving in a
positive direction? (Enter your answer using interval notation.)
(e) Find the total distance...

A particle moves according to a law of motion , , where is
measured in seconds and in feet. Find the velocity at time . What
is the velocity after second? When is the particle at rest? When is
the particle moving in the positive direction? Find the total
distance traveled during the first seconds. Draw a diagram like
Figure 2 to illustrate the motion of the particle. Find the
acceleration at time and after second. Graph Icon Graph the...

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...

If the acceleration of a particle is given by a(t)=2t-1 and the
velocity and position at time t=0 are v(0)=0 and S(0)=2.
1. Find a formula for the velocity v(t) at time t.
2. Find a formula for the position S(t) at time t.
3. Find the total distance traveled by the particle on the
interval [0,3].

Find the total distance traveled by a particle according to the
velocity function v(t)=−t+7 m/sec over the time interval [4,12].
Enter your answer as an exact fraction if necessary and do not
include units in your answer.

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