Top-fuel dragsters like the one shown above accelerate from rest at a tremendous rate. They race on a straight 1/4 mile long track. From a standing start, they complete the quarter mile in about 4.5 seconds and reach a speed of about 330 mph by the finish line.
Part A
Show that the statistics given in the problem introduction are inconsistent at the 10% level with the assumption that the dragster produces constant acceleration as it moves down the track.
System: Dragster as point particle.
Interactions: External influence from the ground (friction) assumed to produce constant acceleration.
Model: [One-Dimensional Motion with Constant Acceleration].
Approach: We are asked to prove that the model we are examining does not fit the data. To do so, we look for a contradiction. In this case, we have several ways to find the acceleration, since we have a large number of givens. Choosing our coordinates such that the race begins at x_
= 0 and proceeds in the positive x direction, we have:
\begin
[ t_
= 0][t_
=\mbox
][ x_
= 0][x_
= \mbox
][v_
= 0][v_
= \mbox
]\end