
Velocity
and Distance for Constant Force Answers
Graph the equation
v = at + v_{0 } over the domain of 0 < t <
4 hours where a= 10 mph^{2} and v_{0}= 100 mph.
 What does the velocity
intercept represent? The initial velocity
of 100 mph.
 Calculate the slope
of the graph. 10 mph^{2}
 What does the slope
represent? Acceleration.
 What is your velocity
after four hours?140 mph
Does this make sense?Yes
 What happens to
your graph if v_{0} = 0? The entire
graph (straight line) shifts downward to a parallel line whose velocity
intercept is zero.
 What effect does
a change in acceleration a have upon your graph? It
changes the slope.
 Using the equation
x = 1/2 at^{2} + v_{0}t + x_{0 }with an x_{0
}=50 miles, graph x over the domain of 0 < t <
4 hours.
Is this a reasonable domain for this equation? The
force will not remain constant for an appreciable time because lift
and drag depend upon the square of the velocity. Although our acceleration
is relatively small, we are changing the velocity a significant amount
in four hours so we probably have assumed too large a domain.
