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Leona [35]
2 years ago
13

A particle is moving with acceleration a ( t ) = 18 t + 16 . Its position at time t = 0 is s ( 0 ) = 10 and its velocity at time

t = 0 is v ( 0 ) = 16 . What is its position at time t = 8 ?
Mathematics
1 answer:
MatroZZZ [7]2 years ago
3 0

Answer:

s(8)=2186

Step-by-step explanation:

A particle is moving with acceleration modeled by the function:

a(t)=18t+16

We are given that its position s(t) at <em>t</em> = 0 is 10 and that its velocity v(t) at <em>t</em> = 0 is 16.

And we want to find its position at <em>t</em> = 8.

Velocity is the integral of the acceleration. Hence:

\displaystyle v(t)=\int a(t)\, dt=\int 18t+16\, dt

Find the velocity. Remember the constant of integration!

v(t)=9t^2+16t+C

Since v(t) is 16 when <em>t</em> = 0:

(16)=9(0)^2+16(0)+C\Rightarrow C=16

Hence, our velocity is given by:

v(t)=9t^2+16t+16

Position is the integral of the velocity. Hence:

\displaystyle s(t)=\int v(t)\, dt=\int 9t^2+16t+16\, dt

Integrate:

\displaystyle s(t)=3t^3+8t^2+16t+C

s(t) is 10 when <em>t</em> = 10. Hence:

C=10

So, our position function is:

s(t)=3t^3+8t^2+16t+10

The position at <em>t</em> = 8 will be:

s(8)=3(8)^3+8(8)^2+16(8)+10=2186

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