## 20121013

### 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.

• 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:
Blank.
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.