Question

The velocity function of a particle is given by v(t) = 3t2 – 24t + 36.

a) Find the equation for a(t), the acceleration.

b) If s(1) = 50, find the displacement function s(t).

c) When will the velocity be zero?

d) Find the distance the particle travels on [0, 4].

Answer #1

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...

17. The velocity function, in feet per second, is given for a
particle moving along a straight line.
v(t) = t2 − t − 132, 1 ≤ t ≤ 15
(a) Find the displacement
(b) Find the total distance that the particle travels over the
given interval.

A particle travels along a straight line with a velocity
v=(12−3t^2) m/s , where t is in seconds. When t = 1 s, the particle
is located 10 m to the left of the origin.
Determine the displacement from t = 0 to t = 7 s.
Determine the distance the particle travels during the time
period given in previous part.

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].

The velocity function, in feet per second, is given for a
particle moving along a straight line. v(t) = t^3 − 10t^2 + 29t −
20, 1 ≤ t ≤ 6 (a) Find the displacement. (b) Find the total
distance that the particle travels over the given interval (solve
in fraction form).
a.) displacement ANSWER IS 175/12 Correct: Your answer is
correct.
b.) Find total displacement. (I only need to solve part B).
=?

The acceleration of an object (in m/s2) is
given by the function a(t)=6sin(t). The initial velocity of the
object is v(0)= −1 m/s. Round your answers to four decimal
places.
a) Find an equation v(t) for the object velocity.
v(t)= -6cos(t)+5
b) Find the object's displacement (in meters) from time 0 to
time 3.
15-6sin(3) Meters
c) Find the total distance traveled by the object from time 0 to
time 3.
? Meters
Need Help fast, please

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...

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...

1. The velocity of a particle moving in a straight line is given
by the function v (t) = 1.0t ^ 2 + 5.0 (m / s). Find the total
displacement of the particle from t = 0 to t = 5.0 (s) using the
definite integral of the function.
2. Find the position function for the following velocity function
at t = 7.2t + 5.4 (m / s2), where we know that the initial velocity
of the particle is...

The velocity v of a particle moving in the
xy plane is given by
v = (7.0t
-4.0t2 )i +
7.5j, in m/s. Here v is
in m/s and t (for positive time) is in s. What is
the acceleration when t = 3.0 s?
i-component of acceleration?
j-component of acceleration?
When (if ever) is the acceleration zero (enter time in
s or 'never')?
When (if ever) is the velocity zero (enter time in s or
'never')?

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