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.
$s\left(t\right)=9t-t^2$, $0\le t\le3$

105. 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 (c) Acceleration equal to zero?

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 (d) When is the acceleration positive? Negative?

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?

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.

$s\left(t\right)=\frac{30}{t+5}$, $-4\le t\le0$

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.

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