Given the position equation $s\(\left\)(t\(\right\))$ , calculate the average velocity (in meters per second) based on the given time interval, and the instantaneous velocity (in meters per second) at the end of the time interval.
$s\(\left\)(t\(\right\))=\(\frac{30}{t+5}\)$, $-4\(\le\) t\(\le\)0$

Which of the following best describes the gradient vector field of the function $f(x,y)=x^2+y^2$?

Terminal velocity Refer to Exercises 95 and 96.

a. Compute a jumper’s terminal velocity, which is defined as lim t → ∞ v(t) = lim t → ∞ √(mg/k) tanh (√(kg/m) t).

Terminal velocity Refer to Exercises 95 and 96.

d. How tall must a cliff be so that the BASE jumper (m = 75 kg and k = 0.2) reaches 95% of terminal velocity? Assume the jumper needs at least 300 m at the end of free fall to deploy the chute and land safely.

Given the position equation $s\(\left\)(t\(\right\))$, calculate the average velocity (in meters per second) based on the given interval, and the instantaneous velocity (in meters per second) at the end of the time interval.

$s\(\left\)(t\(\right\))=9t-t^2$, $0\(\le\) t\(\le\)3$

Given the position of an object $s\(\left\)(t\(\right\))=12t-t^2$ (in meters), find the acceleration of the object at $t=5$ seconds.

Given below is the graph of velocity with respect to time. At which time(s) would acceleration be 0?

Position, velocity, and acceleration Suppose the position of an object moving horizontally along a line after t seconds is given by the following functions s = f(t), where s is measured in feet, with s > 0 corresponding to positions right of the origin.

a. Graph the position function.

$f\left(t\right)=6t^3+36t^2-54t;0\le t\le 4$

{Use of Tech} A damped oscillator The displacement of a mass on a spring suspended from the ceiling is given by $y=10e^{-\frac{t}{2}}\cos \left(\frac{\pi t}{8}\right)$.

a. Graph the displacement function.