Question

1. The distance, in meters, traveled by a moving particle in t seconds is given by d(t)=9t(t+3). Estimate the instantaneous velocity at t=3 seconds using difference quotients with h=0.1, 0.01, and 0.001. If necessary, round the difference quotients to no less than six decimal places and round your final answer to the nearest integer.

Answer #1

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The position of a particle moving with constant acceleration is
given by x(t) = 2t2 +
8t + 4 where x is in meters and t is in
seconds.
(a) Calculate the average velocity of this particle between
t = 6 seconds and t = 9 seconds.
(b) At what time during this interval is the average
velocity equal to the instantaneous velocity?

The position of a particle moving with constant acceleration is
given by
x(t) = 4t2 + 3t +
4
where x is in meters and t is in seconds.
(a) Calculate the average velocity of this particle between
t = 2 seconds and t = 7 seconds.
(b) At what time during this interval is the average velocity equal
to the instantaneous velocity?
(c) How does this time compare to the average time for this
interval?
a. It is larger....

The velocity function (in meters per second) is given for a
particle moving along a line.
v(t) =
t2 − 2t −
8, 1 ≤ t ≤ 5
(a) Find the displacement. (m)
(b) Find the distance traveled by the particle during the given
time interval. (m)

) 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?

Given: v(t) = 6t - 6, on .
The velocity function (in meters per second) is given
for a particle moving along a line. Find the total (left and
right) distance traveled by the particle during the
given time interval from t = 0 to t = 5.

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.

please do 1,2 and 3 thanks
1.The position of a particle moving along the x axis is
given in centimeters by x = 9.12 + 1.75
t3, where t is in seconds. Calculate
(a) the average velocity during the time interval
t = 2.00 s to t = 3.00 s; (b)
the instantaneous velocity at t = 2.00 s;
(c) the instantaneous velocity at t =
3.00 s; (d) the instantaneous velocity at
t = 2.50 s; and (e) the...

Velocity of a Motorcycle The distance s (in feet) covered by a
motorcycle traveling in a straight line and starting
from rest in t sec is given by the function
s(t) = −0.1t3 + 4t2 + 26t (0 ≤ t ≤ 3)
Calculate the motorcycle's average velocity (in ft/sec) over the
time interval [2, 2 + h] for h = 1, 0.1, 0.01, 0.001,
0.0001, and 0.00001. (Round your answers to four decimal
places.)
h = 1 ___________
h =...

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.

Question #3: (4 pts per part) Show all steps to receive
credit.
(a) Suppose a particle is moving along a straight line with
velocity ??(??) = 2?? − 6 in meters per second. Find the total
distance traveled by the particle from t = 1 to t = 6 seconds.
(b) Suppose a particle is moving along a straight line with
velocity ??(??) = 2?? − 6 in meters per second. What is the average
velocity of the particle between...

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