AP Calculus BC / Unit 8: Applications of Integration

8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals

3 practice questions

Notes

Displacement: $\displaystyle \int_a^b v(t)\,dt$.
Total distance: $\displaystyle \int_a^b |v(t)|\,dt$.
Position: $\displaystyle x(b)=x(a)+\int_a^b v(t)\,dt$.
Velocity: $\displaystyle v(b)=v(a)+\int_a^b a(t)\,dt$.

Practice

$v(t)=t-2$ on $[0,4]$. The displacement is:

Using the same $v$, the total distance is:

$x(1)=3$ and $\displaystyle \int_1^5 v(t)dt=-2$. Find $x(5)$.

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