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Researcher
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Reporter:
Skeptic
MOTION
Speed and distance are quantities
measurable by an automobile’s
speedometer (and odometer). That is to
say, the readings correspond to the
instantaneous speed and the distance
traveled (or distance, for short).
For the following questions, think of your car’s speedometer readings.
Can a distance-time graph ever have a negative slope? Why?
Can a speed – time graph ever have a negative slope? Why?
Can the speed or distance ever be negative? Why?
Graphs and motion
Now suppose you are given the displacement-time graph below. Sketch the velocitytime graph from it.
[5 minutes page]
What do you need to know in order to determine the
following quantities? The diagram at right is one example
you may use to test your ideas against.
Distance traveled
Position
Displacement
Average Velocity
Instantaneous speed
Instantaneous velocity
[15 minutes this page]
Graphs to Equations – the Algebra model
Now that we have explored using graphs, and some of the various quantities needed
to describe motion, we can use the graphs to find the coresponding equations which
can be used to calculate motion.
Acceleration = 0
The following velocity and displacement graphs are for the case where there is no
acceleration (think of the level air trak)
Plot the velocity graph here.
Write equations for the displacement and for the velocity in this case
(VERYsimple!).
Constant Acceleration ≠ 0
1. Velocity > 0
Plot the acceleration here.
Remember acceleration = (change in velocity)/time.
Describe in words how to calculate the acceleration from the velocity graph.
Write an equation involving displacement(d) at 6 seconds, time(t), initial
velocity(Vo) and velocity at 6 seconds (Vf).
Sketch a graph of the displacement, starting at x=0, corresponding to the velocity
graph above.
2. Velocity opposite acceleration. (deceleration)
Suppose a ball which floats is thrown downward into water. It has an initial
velocity of 1 m/s downward and an acceleration of 0.5 m/s2 upward.
Choose a positive and negative direction (up or down) and graph the velocity as a
function of time for four seconds.
Now look at your equations and write down the equation for the displacement as a
function of time using the acceleration, initial velocity, your choice of sign and
variable t.
Which of the following graphs would be consistent with your equation? What do
the other two graphs represent?
Sketch the graphs from the demo of a ball being tossed in the air:
Velocity
Displacement
Compare these with your description; are there discrepancies?
How can you revise your description to eliminate the disagreement?
What do you predict for the acceleration now?
Sketch the graph from the demo below.
acceleration
Constant acceleration examples:
[a] A group has been to a party and had too much to drink. As they walked home,
they came to a cliff. It was too dark to see how far it was to the bottom, but they
didn’t remember any deep ravines on the way there. They decide to drop Russel
Yent over the edge and time his fall to the bottom (from the start of the scream
to when it stops). “Besides”, they said to Russ, “what are you worried about, you’re
a bouncer aren’t you?” Russ’s fall took 0.3 seconds. Using 10 m/s for the
acceleration of gravity, how far did Russ fall?
[b] A ball is tossed straight up at an initial velocity of 2 m/s. It rises, then falls
back to the point of launch.
Describe, in words, the acceleration and velocity of the ball during this motion.
Other problems may have different accelerations for different parts of the
problem. Divide and conquer! Split the problem into parts with constant
acceleration. A typical case is a jumping problem.
A frog jumps straight up from the ground and reaches a height of 0.8 m.
Use g = 10 m/s2. If the frog’s feet left the ground 0.1 seconds after the jump
started, calculate the velocity the frog had when it left the ground (from the
height) and the acceleration of the frog while it was pushing off the ground.
More in Conference!