Calculus for AP

Educators

ZZ

Problem 1

A ball dropped from a state of rest at time $t=0$ travels a distance $s(t)=4.9 t^{2} \mathrm{m}$ in $t$ seconds.
(a) How far does the ball travel during the time interval $[2,2.5] ?$
(b) Compute the average velocity over $[2,2.5].$
(c) Compute the average velocity for the time intervals in the table and estimate the ball's instantaneous velocity at $t=2$.

Foster W.

Problem 2

A wrench released from a state of rest at time $t=0$ travels a distance $s(t)=4.9 t^{2} \mathrm{m}$ in $t$ seconds. Estimate the instantaneous velocity at $t=3$.

Dishary H.

Problem 3

Let $v=20 \sqrt{T}$ as in Example $2 .$ Estimate the instantaneous rate of change of $v$ with respect to $T$ when $T=300 \mathrm{K}$.

Foster W.

Problem 4

Compute $\Delta y / \Delta x$ for the interval $[2,5],$ where $y=4 x-9 .$ What is the instantaneous rate of change of $y$ with respect to $x$ at $x=2 ?$

Dishary H.

Problem 5

A stone is tossed vertically into the air from ground level with an initial velocity of 15 $\mathrm{m} / \mathrm{s} .$ Its height at time $t$ is $h(t)=$ $15 t-4.9 t^{2} \mathrm{m}$.

Compute the stone's average velocity over the time interval $[0.5,2.5]$ and indicate the corresponding secant line on a sketch of the graph of $h(t)$ .

Foster W.

Problem 6

A stone is tossed vertically into the air from ground level with an initial velocity of 15 $\mathrm{m} / \mathrm{s} .$ Its height at time $t$ is $h(t)=$ $15 t-4.9 t^{2} \mathrm{m}$.

Compute the stone's average velocity over the time intervals $[1,1.01],[1,1.001],[1,1.0001]$ and $[0.99,1],[0.999,1],[0.9999,1],$ and then estimate the instantaneous velocity at $t=1$.

Dishary H.