Answer:
Step-by-step explanation:
A particle is moving with acceleration modeled by the function:
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:
Find the velocity. Remember the constant of integration!
Since v(t) is 16 when <em>t</em> = 0:
Hence, our velocity is given by:
Position is the integral of the velocity. Hence:
Integrate:
s(t) is 10 when <em>t</em> = 10. Hence:
So, our position function is:
The position at <em>t</em> = 8 will be:
