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 ?

Step-by-step explanation:

A particle is moving with acceleration modeled by the function:

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

And we want to find its position at t = 8.

Velocity is the integral of the acceleration. Hence:

Find the velocity. Remember the constant of integration!

Since v(t) is 16 when t = 0:

Hence, our velocity is given by:

Position is the integral of the velocity. Hence:

Integrate:

s(t) is 10 when t = 10. Hence:

So, our position function is:

The position at t = 8 will be:

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step-by-step explanation: