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

106. Motion Along a Line The graphs in Exercises 105 and 106 show the position s=f(t) of an object moving up and down on a coordinate line. At approximately what times is the (b) velocity equal to zero?

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The accompanying figure shows the velocity v = ds/dt = f(t) (m/sec) of a body moving along a coordinate line.

a. When does the body reverse direction?

Suppose the position of a particle moving along a straight line is given by the graph below. At time $t=2$ seconds, estimate the value of the velocity and acceleration of the particle using the graph.

Given the vector-valued function $r\left(t\right)=(t^2,\frac{2}{3}{t}^3,t)$, find the unit tangent vector $T$, the unit normal vector $N$, and the unit binormal vector $B$ at the point $(4,\frac{-16}{3},-2)$. Which of the following correctly gives the unit tangent vector $T$ at that point?

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 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$