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Unformatted text preview: distance required for the Aero TT to stop. Compare
this distance to the corresponding distance in the absence of air drag (i.e. just kinetic road friction).
(c) If the blocking car was removed when the car had slowed to a velocity of 200 Km/h and then the driver
starts accelerating again with constant maximum force, what is the velocity that the Aero TT reaches
after it travels a distance of 2 Km from the point it started re-accelerating? (Brieﬂy, discuss)
(d) Make a rough sketch (by hand, not with Mathematica!) of the car’s position x(t) described by the
“story” of parts b and c (i.e., starting from when the driver entered the straight track, and ending at
the ﬁnal position after part c.) Comment brieﬂy on interesting features of your graph (e.g., signs of
slope, signs of concavity, interesting points...)
2. (a) In Taylor’s book, he simpliﬁes Eqn 2.42 for the range of a projectile by assuming that R2 ∼ Rvac .
Show that if instead you use the quadratic equation to solve for R directly in Eqn 2.42, and make the
appropriate Taylor series expansion, that you obtain the expression given in Equation 2.44. (b) If you use your result from the previous part to compute R when vy0 = vter , what do you get? Does
this make sense? (Brieﬂy, discuss) (2 pts)
3. Recall from special relativity that for a particle moving at a relativistic speed, v , the energy E = γ mc2 , where
γ = √ 1 2 2 . Find the ﬁrst two terms of the Taylor series expansion of the energy, in the non-relativistic
(1−v /c ) limit v << c. What is the second term? Does this make sense? CONTINU...
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