What is the slope of a graph?
Reading: The slope
of a straight line graph which can be easily
defined as the rise
divided by the run
. If the graph is curved,
the slope at each point can be calculated from the tangent line at each
point. It is easy to see that the speed-time graph can be obtained from
the slope of the distance-time graph, and the acceleration-time graph can
be constructed from the speed-time graph. Thus the distance-time graph contains
all the information about the motion of an object.
Objects near the surface of the earth always accelerate or decelerated
at a rate of 9.8 m/s/s.
- An object is thrown straight up. What is the instantaneous speed of the object at the top of its path? What is the acceleration of the object at the top of its path?
- A brick falls freely from a high scaffold. What is its speed in m/s after 4.0 s? How far does the brick fall during the first 4.0 seconds.
- A mortar shell is shot straight up with an initial speed of 98 m/s. How long does the shell remain in the air? How high does the shell rise?
- A stone falls freely from rest for 8.0 seconds. What is the final speed? What distance does the stone fall during this time?
- During a baseball game a batter hits a ball straight up and it remains in the air for 6.0 seconds. How high did the ball go?
- A plane files in a straight line with a constant speed of 50 m/s. Construct a table showing the total distance the plane travels at the end of each second for a 20-s period. Plot a distance-time graph. Show that the slope of the graph gives the speed of the plane. Plot the speed-time graph of the plane's motion.
- Sketch the distance-time, speed-time, and acceleration-time graphs for constant speed and uniform acceleration for a total of six graphs.