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?

Understanding Motion from Graphs

The accompanying figure shows the velocity v = f(t) of a particle moving on a horizontal coordinate line.

b. When is the particle’s acceleration positive? Negative? Zero?

Understanding Motion from Graphs

The accompanying figure shows the velocity v = f(t) of a particle moving on a horizontal coordinate line.

c. When does the particle move at its greatest speed?

Understanding Motion from Graphs

The accompanying figure shows the velocity v = f(t) of a particle moving on a horizontal coordinate line.

d. When does the particle stand still for more than an instant?

Finding g on a small airless planet Explorers on a small airless planet used a spring gun to launch a ball bearing vertically upward from the surface at a launch velocity of 15 m/sec. Because the acceleration of gravity at the planet’s surface was gₛ m/sec², the explorers expected the ball bearing to reach a height of s = 15t − (1/2)gₛt² m t sec later. The ball bearing reached its maximum height 20 sec after being launched. What was the value of gₛ?

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 interval, and the instantaneous velocity (in meters per second) at the end of the time interval.

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