Velocity and Acceleration A car travels in a straight line for 1 hour. Its velocity v in miles per hour at six-minute intervals is shown in the table. t (hours ) 0 0.1 0.2 0.3 0.4 0.5 v (mi/h ) 0 10 20 40 60 50 t (hours ) 0.6 0.7 0.8 0.9 1.0 v (mi/h ) 40 35 40 50 65 (a) Produce a reasonable graph of the velocity function v by graphing these points and connecting them with a smooth curve. (b) Find the open intervals over which the acceleration a is positive. (c) Find the average acceleration of the car (in miles per hour per hour) over the interval [0, 0.4]. (d) What does the integral ∫ 0 1 v ( t ) d t signify? Approximate this integral using the Midpoint Rule with five subintervals. (e) Approximate the acceleration at t = 0.8
Velocity and Acceleration A car travels in a straight line for 1 hour. Its velocity v in miles per hour at six-minute intervals is shown in the table. t (hours ) 0 0.1 0.2 0.3 0.4 0.5 v (mi/h ) 0 10 20 40 60 50 t (hours ) 0.6 0.7 0.8 0.9 1.0 v (mi/h ) 40 35 40 50 65 (a) Produce a reasonable graph of the velocity function v by graphing these points and connecting them with a smooth curve. (b) Find the open intervals over which the acceleration a is positive. (c) Find the average acceleration of the car (in miles per hour per hour) over the interval [0, 0.4]. (d) What does the integral ∫ 0 1 v ( t ) d t signify? Approximate this integral using the Midpoint Rule with five subintervals. (e) Approximate the acceleration at t = 0.8
Solution Summary: The author illustrates the velocity function v by graphing the provided points (hours) and connecting them with a smooth curve.
Velocity and Acceleration A car travels in a straight line for 1 hour. Its velocity v in miles per hour at six-minute intervals is shown in the table.
t (hours)
0
0.1
0.2
0.3
0.4
0.5
v (mi/h)
0
10
20
40
60
50
t (hours)
0.6
0.7
0.8
0.9
1.0
v (mi/h)
40
35
40
50
65
(a) Produce a reasonable graph of the velocity function v by graphing these points and connecting them with a smooth curve.
(b) Find the open intervals over which the acceleration a is positive.
(c) Find the average acceleration of the car (in miles per hour per hour) over the interval [0, 0.4].
(d) What does the integral
∫
0
1
v
(
t
)
d
t
signify? Approximate this integral using the Midpoint Rule with five subintervals.
(e) Approximate the acceleration at
t
=
0.8
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Automobile Department
Subject :Engineering Analysis
Time: 2 hour
Date:27-11-2022
کورس اول تحليلات
تعمیر )
1st month exam / 1st semester (2022-2023)/11/27
Note: Answer all questions,all questions have same degree.
Q1/: Find the following for three only.
1-
4s
C-1
(+2-3)2 (219) 3.0 (6+1)) (+3+5)
(82+28-3),2-
,3-
2-1
4-
Q2/:Determine the Laplace transform of the function t sint.
Q3/: Find the Laplace transform of
1,
0≤t<2,
-2t+1,
2≤t<3,
f(t) =
3t,
t-1,
3≤t 5,
t≥ 5
Q4: Find the Fourier series corresponding to the function
0
-5
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Subject :Engineering Analysis
Time: 80 min
Date:11-12-2022
Automobile Department
2nd month exam / 1" semester (2022-2023)
Note: Answer all questions,all questions have same degree.
کورس اول
شعر 3
Q1/: Use a Power series to solve the differential equation:
y" - xy = 0
Q2/:Evaluate using Cauchy's residue theorem,
sinnz²+cosz²
dz, where C is z = 3
(z-1)(z-2)
Q3/:Evaluate
dz
(z²+4)2
Where C is the circle /z-i/-2,using Cauchy's residue theorem.
Examiner: Dr. Wisam N. Hassan
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Subject :Engineering Analysis
Time: 80 min
Date:11-12-2022
Automobile Department
2nd month exam / 1" semester (2022-2023)
Note: Answer all questions,all questions have same degree.
کورس اول
شعر 3
Q1/: Use a Power series to solve the differential equation:
y" - xy = 0
Q2/:Evaluate using Cauchy's residue theorem,
sinnz²+cosz²
dz, where C is z = 3
(z-1)(z-2)
Q3/:Evaluate
dz
(z²+4)2
Where C is the circle /z-i/-2,using Cauchy's residue theorem.
Examiner: Dr. Wisam N. Hassan
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