Find the first and the second derivative of x = }at² + bt + c, where a, b, and c are con- stants. The function gives the position (in m) of a particle in one dimension, where t is the time (in s), a is acceleration (in m/s²), b is velocity (in m/s) at a time t = 0, and c is the po- sition (in m) of the particle at f = 0.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Find the first and the second derivative of x = at? + bt + c, where a, b, and c are con-
stants. The function gives the position (in m) of a particle in one dimension, where t is the
time (in s), a is acceleration (in m/s2), b is velocity (in m/s) at a time t = 0, and c is the po-
sition (in m) of the particle at f = 0.
%3D
PICTURE Both the first and the second derivatives are sums of terms; for each differentia-
tion we take the derivative of each term separately and add the results.
SOLVE
d(}at?)
a 2t = at
1. To find the first derivative, first compute the derivative of the
first term:
dt
d(bt)
= b,
d(c)
= 0
dt
2. Compute the first derivative of the second and third terms:
dt
dx
= at + b
dt
3. Add these results:
4. To compute the second derivative, repeat the process for the
result in step 3:
d²x
= a + 0 = a
dt2
Transcribed Image Text:Find the first and the second derivative of x = at? + bt + c, where a, b, and c are con- stants. The function gives the position (in m) of a particle in one dimension, where t is the time (in s), a is acceleration (in m/s2), b is velocity (in m/s) at a time t = 0, and c is the po- sition (in m) of the particle at f = 0. %3D PICTURE Both the first and the second derivatives are sums of terms; for each differentia- tion we take the derivative of each term separately and add the results. SOLVE d(}at?) a 2t = at 1. To find the first derivative, first compute the derivative of the first term: dt d(bt) = b, d(c) = 0 dt 2. Compute the first derivative of the second and third terms: dt dx = at + b dt 3. Add these results: 4. To compute the second derivative, repeat the process for the result in step 3: d²x = a + 0 = a dt2
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