A car starts from rest and accelerates to a speed of 60 mph in 12 sec. It travels 60 mph for 1 min and then decelerates for 20 sec until it comes to rest. The speed of the car s ( t ) (in mph) at a time t (in sec) after the car begins motion can be modeled by: s ( t ) = { 5 12 t 2 f o r 0 ≤ t ≤ 12 60 f o r 12 < t ≤ 72 3 20 ( 92 − t ) 2 f o r 72 < t ≤ 92 Determine the speed of the car 6 sec, 12 sec, 45 sec, and 80 sec after the car begins motion.
A car starts from rest and accelerates to a speed of 60 mph in 12 sec. It travels 60 mph for 1 min and then decelerates for 20 sec until it comes to rest. The speed of the car s ( t ) (in mph) at a time t (in sec) after the car begins motion can be modeled by: s ( t ) = { 5 12 t 2 f o r 0 ≤ t ≤ 12 60 f o r 12 < t ≤ 72 3 20 ( 92 − t ) 2 f o r 72 < t ≤ 92 Determine the speed of the car 6 sec, 12 sec, 45 sec, and 80 sec after the car begins motion.
Solution Summary: The author evaluates the speed of the car at various given time interval from start time using mathematical methodologies.
A car starts from rest and accelerates to a speed of 60 mph in 12 sec. It travels 60 mph for 1 min and then decelerates for 20 sec until it comes to rest. The speed of the car s(t) (in mph) at a time t (in sec) after the car begins motion can be modeled by:
s
(
t
)
=
{
5
12
t
2
f
o
r
0
≤
t
≤
12
60
f
o
r
12
<
t
≤
72
3
20
(
92
−
t
)
2
f
o
r
72
<
t
≤
92
Determine the speed of the car 6 sec, 12 sec, 45 sec, and 80 sec after the car begins motion.
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Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
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