Find the position function s(t) given the acceleration function and an initial value. a(t)=12-t, v(0)=7, s(0)=0

Giovanna Shaw

Giovanna Shaw

Answered question

2022-11-28

Find the position function s(t) given the acceleration function and an initial value.
a ( t ) = 12 t , v ( 0 ) = 7 , s ( 0 ) = 0

Answer & Explanation

Lokasckf

Lokasckf

Beginner2022-11-29Added 7 answers

a ( t ) = 12 t
Now v ( t ) = a ( t ) d t v ( t ) = ( 12 t ) d t + C v ( t ) = 12 t t 2 2 + C - (1)
Put t=0
v(0)=0-0+c
Given that v(0)=7
c=7
Put value of c in equation (1)
v ( t ) = 12 t t 2 2 + 7
Now s ( t ) = v ( t ) d t
= ( 12 t t 2 2 + 7 ) d t + C s ( t ) = 12 t 2 2 t 3 6 + 7 t + C s ( t ) = 6 t 2 t 3 6 + 7 t + C
Put t=0
s ( 0 ) = 0 0 + 0 + c
Given that s(0)=0
c=0
Put value of C in equation (2)
s ( t ) = 6 t 2 t 3 6 + 7 t

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