The velocity function (in meters per second) for a particle moving along a line is given byv(t) 3t 7, 0 < t < 3.(a) Find the displacement (in meters) of the particle.Displacement =meters(b) Find the total distance traveled (in meters) by the particle.Total distance traveled =meters

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Asked Nov 5, 2019
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The velocity function (in meters per second) for a particle moving along a line is given by
v(t) 3t 7, 0 < t < 3.
(a) Find the displacement (in meters) of the particle.
Displacement =
meters
(b) Find the total distance traveled (in meters) by the particle.
Total distance traveled =
meters
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The velocity function (in meters per second) for a particle moving along a line is given by v(t) 3t 7, 0 < t < 3. (a) Find the displacement (in meters) of the particle. Displacement = meters (b) Find the total distance traveled (in meters) by the particle. Total distance traveled = meters

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Expert Answer

Step 1
To determine the following part of the velocity v(t)-3t-7 for the given interval
a). displacement of the particle
b). total distance traveled by the particle
Given information
v(t) 3t 7, 0 t<3.
Used formula:
Integration formula
(1)
n+1
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To determine the following part of the velocity v(t)-3t-7 for the given interval a). displacement of the particle b). total distance traveled by the particle Given information v(t) 3t 7, 0 t<3. Used formula: Integration formula (1) n+1

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Step 2
calculation:
for part(a)
Displacement of the particle is given below
(t)3t-7
v()dt=£(3-7)df
(from equation 1)
3
- 7t
2
-70-70
27
= -21
2
27-42
2
15
2
15
meter
2
displacement is
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calculation: for part(a) Displacement of the particle is given below (t)3t-7 v()dt=£(3-7)df (from equation 1) 3 - 7t 2 -70-70 27 = -21 2 27-42 2 15 2 15 meter 2 displacement is

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Step 3
calculation
for part(b)
for total distance of the particle find the interval where the velocity is negative and the interval where the velocity is positive
v(t) 3t7
3t 7 0
7
t =-second
3
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calculation for part(b) for total distance of the particle find the interval where the velocity is negative and the interval where the velocity is positive v(t) 3t7 3t 7 0 7 t =-second 3

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Math

Calculus