Question

Suppose the velocity function of a particle is ?(?) =
?^{2} + 3? − 4 (in meters per second). Find the distance
traveled by the particle during the time period 0 ≤ ? ≤ 4. Be sure
to write units for your answer

Answer #1

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)

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.

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...

A particle moves along a line with velocity v(t)=(3 -
t)(2+t), find the distance traveled during the time interval [0,
1].

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.

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 of a particle moving along a line is a function of
time given by v(t)=81/(t2+9t+18). Find the
distance
that the particle has traveled after t=9 seconds if it started at
t=0 seconds.

3. The velocity function of a particle is moving on a coordinate
line is given by ?(?) = 6?^2 − 42? + 60 where ? is in meters per
seconds and ? is in seconds.
a) When is the particle at rest?
b) When does the particle have positive velocity?
c) When does the particle have negative acceleration?
d) When is the particle speeding up?
e) Sketch the position-time graph of the particle and the
acceleration-time graph of the particle...

A) A particle starts from the origin with velocity 5 ?̂m/s at t
= 0 and moves in the xy plane with a varying acceleration given by
?⃗ = (2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared and
t is in seconds.
i) Determine the velocity of the particle as a function of
time.
ii) Determine the position of the particle as a function of
time.
(Explanation please )

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
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