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

Launching a Rocket When a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for a while and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the rocket to keep it from breaking when it lands.

The figure here shows velocity data from the flight of the model rocket. Use the data to answer the following.

d. When did the parachute pop out? How fast was the rocket falling then?

Understanding Motion from Graphs

Launching a Rocket When a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for a while and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the rocket to keep it from breaking when it lands.

The figure here shows velocity data from the flight of the model rocket. Use the data to answer the following.

f. When was the rocket’s acceleration greatest?

Understanding Motion from Graphs

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

a. When does the particle move forward? Move backward? Speed up? Slow down?

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.

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?

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?