Physics midterm question: cars braking

Physics 205A Midterm 1, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 2.11, 2.25

[10 points.] Two cars are initially traveling side-by-side with the same speed in the forward direction along a straight horizontal road. Both cars apply their brakes at the same time, such that they slow down with different accelerations until they each come to a complete stop. Describe/show how the vx(t) graph at right should be changed such that it correctly describes this situation. Explain your reasoning by using the properties of position, displacement, velocity, and acceleration.

Solution and grading rubric:
  • p = 10/10:
    Correct. Describes/shows two lines with different slopes, with same initial velocity at same initial time, and zero velocities at different times.
  • r = 8/10:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t = 6/10:
    Nearly correct, but argument has conceptual errors, or is incomplete. At least understands how initial and final velocity, acceleration and displacement information is represented on a vx(t) graph.
  • v = 4/10:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  • x = 2/10:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y = 1/10:
    Irrelevant discussion/effectively blank.
  • z = 0/10:

Grading distribution:
Sections 70854, 70855
Exam code: midterm01w4Sh
p: 48 students
r: 1 student
t: 3 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 4816):

Another sample "p" response (from student 5950), showing some of the (identical) behavior of the cars before brakes were applied:

Yet another sample "p" response (from student 6666), with perhaps a more realistic depiction of deceleration due to anti-lock brakes:

No comments: