## 20111018

### 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.

• 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:
Blank.

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: