To practice Tactics Box 1.5 Drawing a Pictorial Representation. You will find that motion problems and other physics problems often have several variables and other pieces of information to keep track of. The best way to tackle such problems is to draw a pictorial representation of the problem that shows all of the important details. This Tactics Box explains how to draw a pictorial representation of a motion problem.
TACTICS BOX 1.5 Drawing a pictorial representation
1. Draw a motion diagram. The motion diagram develops your intuition for the motion.
2. Establish a coordinate system. Select your axes and origin to match the motion. For one-dimensional motion, you want either the x-axis or the y-axis
parallel to the motion. The coordinate system determines whether the signs of v and a are positive or negative.
3. Sketch the situation. Not just any sketch. Show the object at the beginning of the motion, at the end, and at any point where the character of the motion
changes. Show the object, not just a dot, but very simple drawings are adequate.
4. Define symbols. Use the sketch to define symbols representing quantities such as position, velocity, acceleration, and time. Every variable used later in the
mathematical solution should be defined on the sketch. Some will have known values, and others are initially unknown, but all should be given symbolic
names.
5. List known information. Make a table of the quantities whose values you can determine from the problem statement or that can be found quickly with
simple geometry or unit conversions. Some quantities are implied by the problem, rather than explicitly given. Others are determined by your choice of
coordinate system.
6. Identify the desired unknowns. What quantity or quantities will allow you to answer the question? These should have been defined as symbols in step 4.
Don’t list every unknown, only the one or two needed to answer the question.
Follow the steps above to draw a pictorial representation of the following problem: A light train is traveling on a straight section of track at a constant speed of 15 \rm m/s.
As it approaches the next station, it starts to slow down at a rate of 5 \rm m/s^2 until it stops at the station. From the moment the train starts to slow down, how long does it
take for the train to reach the station? Note that you are not expected to solve this problem, only to draw the pictorial representation.
Draw a motion diagram for the train. Assume that the train is moving toward the right and starts to slow down at t = 0. The separation of each dot represents an elapsed time of one second. Include velocity vectors and the acceleration vector in your drawing. Keep in mind that the acceleration of the train has a magnitude of 5 {\rm m/s^2}.
The orientation and length of the velocity vectors will be graded. Only the direction of the acceleration vector will be graded. The location of the vectors will not be graded.