13. submit answer practice similar the velocity of a car is f(t)=11t meters/second. use a graph of f(t) to…

Explanation:

Step1: Recall the distance - velocity relationship

The distance $d$ traveled by an object with velocity function $v = f(t)$ from $t=a$ to $t = b$ is given by $d=\int_{a}^{b}f(t)dt$. Here, $f(t)=11t$, $a = 0$, and $b = 10$.

Step2: Calculate the definite integral

We need to evaluate $\int_{0}^{10}11t\ dt$. Using the power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), we have $\int_{0}^{10}11t\ dt=11\int_{0}^{10}t\ dt$. Then $11\times\left[\frac{t^{2}}{2}\right]_{0}^{10}$.

Step3: Evaluate the definite integral

First, substitute the upper and lower limits: $11\times\left(\frac{10^{2}}{2}-\frac{0^{2}}{2}\right)$. Since $\frac{0^{2}}{2}=0$ and $\frac{10^{2}}{2}=\frac{100}{2}=50$, we get $11\times50 = 550$.

Answer:

$550$ meters