June 6, 1997

Physics 211 - This question is a continuation of the May 30 question. Remember that in that question we had one car whose position x at time t was given by x = -20t + 20. Let us call this Car A. Suppose there is a second car, Car B, which is parked on the road at x = 10 m.

(a) At what time does Car A pass Car B? Determine the answer both graphically and analytically. (Graphs. Analytical Geometry.)

(b) Show the graphs of the motions of Cars A and B in the reference frame of Car A, i.e., on a pair of x',t axes where the x'-axis is the position axis relative to which Car A is at rest. As in the May 30 question, Car A is at x' = 20 m. Draw the x'-axis vertical and the t-axis horizontal.

Is the intersection point of the x' vs. t graphs for the two cars consistent with the answer in part (a)?(Graphs. Analytical Geometry.)

Question of the Week - June 13, 1997

Physics 211 - This question and the following ones until July 11, 1997 will deal with signs, notation, terminology, and graphs, all related to position, displacement, and distance travelled. (Analytical Geometry.)

The following diagram shows two points, P₁ and P₂, on an x-axis. The x-coordinates of the two points are denoted x₁ and x₂, respectively.

Definitions. Suppose an object moves from P₁ to P₂, then the displacement of the object is defined as the change in position, i.e., as the difference x₂ - x₁. This difference is also denoted Dx = x₂ - x₁ (read: "delta x"). This displacement must be distinguished from the distance travelled by the object, which is equal to the distance between the two points and which in turn is equal to the absolute value |x₂ - x₁|.

Note that a distance between two points and the distance travelled by an object can never be negative, but that a displacement can be negative.

Question. In the diagram above, the direction of the x-axis is to the right, i.e., the x-values are increasing as one goes to the right. (This is indicated by having the x-label of the axis on the right.) Suppose the points P₁ to P₂ remain unchanged, but that the direction of the x-axis is reversed. What are the signs of the displacement Dx = x₂ - x₁ and of the distance travelled by the object, |x₂ - x₁| then? I.e., indicate which ones, if any, of these quantities are positive and which ones are negative.

Question of the Week - June 20, 1997

Physics 211 -

Please refer back to the June 13, 1997 Question. It is available in the Question Archive. (Analytical Geometry. Graphs.)

Draw graphs of (a) position x vs. time t, (b) the corresponding displacement Dx vs. time t, and (c) the corresponding distance s travelled vs. time t for motions from P₁ to P₂ and back to P₁ and for motions from P₂ to P₁ and back to P₂. Do this for an x-axis pointing to the right as in the diagram above and for an x-axis pointing in the opposite direction. That is a total of 12 graphs.

Take x₁ = -10 m and x₂ = 4 m when the x-axis points to the right and x₁ = 10 m and x₂ = -4 m when the x-axis points to the left.

Question of the Week - June 27, 1997

Physics 211 - Please refer back to the June 13, 1997 Question, in particular the definitions of displacement and distance travelled, and to the June 20, 1997 Question, which has examples of graphs. These questions are available in the Question Archive. (Analytical Geometry. Graphs.)

Suppose a hiker leaves his camp at time t = 0 in the morning and returns to his camp two hours later. Various hypothetical graphs of distance travelled, s, vs. time elapsed, t, for the hike are shown above.

Which graph (or graphs) could represent the distance travelled by the hiker vs. time elapsed? Give reasons, both for the possible and the impossible graphs.