Question

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 2.5 (m / s) and that the initial position of the
particle is 1.0 (m).

Answer #1

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m
/ s and its initial displacement is s( 0 ) = 5 m. Find the position
of the particle at t = 1 seconds.

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is: v(0) = 4 m/
and its initial displacement is s(0) = 5 ms. Find the position of
the particle at t = 1 seconds.
10 m
5 m
11 m
4 m
2m

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 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)

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.

The velocity of a particle moving along the x-axis
varies with time according to
v(t) = A +
Bt−1,
where
A = 7 m/s,
B = 0.33 m,
and
1.0 s ≤ t ≤ 8.0 s.
Determine the acceleration (in m/s2) and position (in
m) of the particle at
t = 2.6 s
and
t = 5.6 s.
Assume that
x(t = 1 s) = 0.
t = 2.6 s
acceleration m/s2 position m
?
t = 5.6 s
acceleration m/s2
position m ?

The displacement (in centimeters) of a particle moving back and
forth along a straight line is given by the equation of motion
s = 4 sin(πt) + 5
cos(πt),
where t is measured in seconds. (Round your answers to
two decimal places.)
(a) Find the average velocity during each time period.
(i) [1, 2] cm/s
(ii) [1, 1.1]
cm/s
(iii) [1, 1.01]
m/s
(iv) [1, 1.001]
(b) Estimate the instantaneous velocity of the particle when
t = 1.

A particle is moving along a straight line, and its position is
defined by s = (t2 - 6t +6) m. At t=6 seconds, find the following :
a. the acceleration of the particle b. The average speed c. the
average velocity

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.

The displacement (in centimeters) of a particle moving back and
forth along a straight line is given by the equation of motion
s = 3 sin(πt) + 4
cos(πt),
where t is measured in seconds. (Round your answers to
two decimal places.)
(a) Find the average velocity during each time period.
(i) [1, 2]
cm/s
(ii) [1, 1.1]
cm/s
(iii) [1, 1.01]
cm/s
(iv) [1, 1.001]
cm/s
(b) Estimate the instantaneous velocity of the particle when
t = 1.
cm/s

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