Physics midterm question: side-by-side(?) cars

Physics 205A Midterm 1, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 2.11

Two cars are momentarily traveling side-by-side as they both travel in the +x direction at t = 0. Describe/show how the vx(t) graph at right indicates that the cars are not side-by-side at t = 80 s. Explain your reasoning by using the properties of position, displacement, velocity, and acceleration.

Solution and grading rubric:
  • p:
    Correct. Understands that displacement (which here is equal to distance traveled, as there is only straight-line motion in the same direction) is the area of a vx(t) graph, and since the area under car 2 is greater than car 1, then car 2 has traveled a farther distance than car 1 from t = 0 to 80 s, and thus car 2 is ahead of car 1 at t = 80 s.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. Some plausible connection made between velocity and distance traveled using kinematic equations for constant acceleration motion and/or integral/differential calculus.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some applicaiton of kinematic equations for constant acceleration motion and/or integral/differential calculus, typically focus is on difference of slopes/accelerations.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 70854, 70855
Exam code: midterm01sWFf
p: 16 students
r: 6 students
t: 7 students
v: 28 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1223):

Another sample "p" response (from student 3548), calculating how much car 1 and car 2 have each traveled since they were side-by-side.

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