Question

Suppose the position of a particle is given
s(t)=(1/3)t^{3} - t^{2} - 8t + 10. Determine the
following

A) What is the velocity function v(t)=

B) What is the acceleration function a(t)=

C) What is the object at rest t=

D) What is the position of the object at rest? Be sure to enter your answer as an exact fraction s=

Answer #1

The position of a particle is given by x = (t3)/3 +
t2 - 8t - 4 and y = t2 + 8t + 3.
1) When, if ever is the particle's SPEED is constant?
Ans: t = 0s, 1s, -4s
2) When is the speed increasing?

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...

1) The position of a particle moving along x direction is given
by: x=8t-3t2.What is the velocity of the particle at t=2
s and what is the acceleration?
2) A roller coaster car starts from rest and descends
h1= 40 m. The car has a mass of 75 kg. What is the speed
at 20m while going down the hill?

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 − 9t2
+ 15t
(a) Find the velocity at time t.
v(t) =
(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...

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].

1-The velocity of a particle is v = { 6 i + (
28 - 2 t ) j } m/s, where t is in seconds. If r=0
when t=0, determine particle displacement during time interval t =
3 s to t = 8 s in the y direction.
2-A particle, originally at rest and located at point (1 ft, 4
ft, 5 ft), is subjected to an acceleration of a={ 3 t
i + 17 t2k} ft/s.
Determine magnitude...

) A particle is moving according to the velocity equation v(t) =
9t^2-8t-2 . The equation uses units of meters and seconds
appropriately. At t = 1 s the particle is located at x = 2 m. (a)
What is the particle's position at t = 2 s? (b) What is the
particle's acceleration at t = 1 s? (c) What is the particle's
average velocity from t = 2 s to t = 3 s?

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...

The position function of a moving particles is give by r(t) =
[(5 m.s-1)t + (6 m.s-2)t2]
i + [(7.0 m) - (3
m.s-3)t3] j.
Calculate:
(i) the displacement of the particle from t = 2 s to t = 3 s.
(ii) The instantaneous velocity and acceleration at t = 3 s.

The position of a particle for t > 0 is given by →r (t) =
(3.0t 2 i ^ − 7.0t 3 j ^ − 5.0t −2 k ^ ) m. (a) What is the
velocity as a function of time? (b) What is the acceleration as a
function of time? (c) What is the particle’s velocity at t = 2.0 s?
(d) What is its speed at t = 1.0 s and t = 3.0 s? (e) What is...

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