Lecture Thirteen Practice

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Practice problems for Lecture Thirteen Content

1 : The position $s(t)$ of a robot moving along a track at time $t$ is given by $s(t) = 8t^{2} + 64t + 6$ . What is the velocity $v(t)$ of the particle at time $t$ ?

$v(t) = \answer {16t + 64}$

1.1 : Find the total distance traveled by the robot between $t = -8$ and $t = 0$ .

$\answer {256}.$

1.1.1 : What is the acceleration $a(t)$ of the particle at time $t$ ? $a(t) = \answer {16}$

1.1.1.1 : On which interval is the robot speeding up? $\left (\answer {-4},\answer {+\infty }\right ).$

2 : The position $s(t)$ of a robot moving along a track at time $t$ is given by $s(t) = 9t^{2} - 90t + 4$ . What is the velocity $v(t)$ of the particle at time $t$ ?

$v(t) = \answer {18t - 90}$

2.1 : Find the total distance travelled by the robot between $t = 0$ and $t = 9$ .

$\answer {369}.$

2.1.1 : What is the acceleration $a(t)$ of the particle at time $t$ ? $a(t) = \answer {18}$

2.1.1.1 : On which interval is the robot speeding up? $\left (\answer {5},\answer {\infty }\right ).$

3 :

At time $t = 0$ , a cannonball is launched, with its height $h$ in meters given by $h(t) = -5t^{2} + 4t + 2$ . At what time $t$ does the cannonball reach its peak?

$\text {peak time $t$} = \answer {\frac {2}{5}}$

3.1 :

What is the height of the cannonball at its peak? $\text {peak time $t$} = \answer {\frac {14}{5}}$

4 : At time $t = 0$ , a cannonball is launched, with its height $h$ in meters given by $h(t) = -5t^{2} + 7t + 4$ . At what time $t$ does the cannonball reach its peak?

$\text {peak time $t$} = \answer {\frac {7}{10}}$

4.1 : What is the height of the cannonball at its peak? $\text {peak time $t$} = \answer {\frac {129}{20}}$