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Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial positiona(t) 8ev(0)-8, and s(0) 9v(t)s(t)

Question
Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position
a(t) 8ev(0)
-8, and s(0) 9
v(t)
s(t)
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Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position a(t) 8ev(0) -8, and s(0) 9 v(t) s(t)

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Step 1

Integrate the acceleration and find the velocity.

v)=alt)
-js
e*dt
-
e
=8
-1
C
=-8e c
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v)=alt) -js e*dt - e =8 -1 C =-8e c

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Step 2

Use the initial condition of the velocity to find the constant of integration c and the velocity.

v(0)-8
-8ec-8
-8 c-8
c 0
=-8e
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v(0)-8 -8ec-8 -8 c-8 c 0 =-8e

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Step 3

Integrate the velocity and...

s)-r)
=f-
8e 'dt
= -8
= 8e c
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s)-r) =f- 8e 'dt = -8 = 8e c

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Calculus

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