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13-141.

Steady Freddy’s cousin Freda always drives with a steadily increasing velocity. Freda’s velocity is given by the function $v\left(t\right) = 10t$, where $t\ge0$.

1. Sketch a graph of Freda’s velocity function.

2. How far has Freda traveled after $1$ hour? After $2$ hours? After $3$ hours?

Since the velocity is not constant, you will need to compute the area under the curve.
In this case use the formula for the area of a triangle.

3. Using your answers to part (b), what is Freda’s position as a function of time?

The area of a triangle is $A = 0.5\left(\text{base}\right)\left(\text{height}\right)$.
What are the expressions for the base and height in this situation?

4. How is Freda’s position function related to her velocity function?

5. How is Freda’s velocity function related to her position function? Use what you learned in previous lessons to justify your answer algebraically.

Assuming your function from part (c) is $s$$v\left(t\right)=s^\prime(t)=\lim \limits _{h \rightarrow 0} \frac{s(t+h)-s(t)}{h}$