Uniform-Motion Problems: Just Playing With Cars

David Drymiller                Morgan Park High School
                               1744 W. Pryor
                               Chicago IL 60643
                               (312)535-2550

Objectives:

     To solve uniform motion word problems using rate X time = distance.
     To practice measuring in the metric and English systems.

Materials Needed:

     At least two battery operated cars with constant velocity,
     Measuring tape with both English and metric systems at least 50 feet or    
     15 meters, meter and yard sticks,
     Stop Watches at least two or more if possible,
     masking tape
        
Strategy:

The students perform the following demonstration for their classmates under the 
direction of the classroom teacher.   No prior knowledge of the activity is 
needed by the students. 

First, with masking tape mark the starting and finishing lines for calculating 
velocity over a fixed distance.  (I used 800 cm.)  Find the time needed for each 
car to transverse the fixed distance.  Record the time and distance on the 
blackboard and then calculate the velocity of each car. 
                                              (25 cm/sec and 36 cm/sec)

Now introduce the first type of Uniform-Motion Problem, "If the cars are place 
back to back and travel at the same time in opposite directions, when will they
be 1000 cm apart?".  Explain the problem first as the cars are placed on the 
floor back to back and run off in opposite directions.  Next use the standard 
associated pictures and charts for this type of problem, write the equation and
solve it in the usual manner.

                               25t + 36t = 1000 
                                     61t = 1000 
                                       t = 16.39
 
Place the cars back to back on the floor and let them run for 16.4 secs. and
measure the distance between the two cars.  (It should work. I got 1020 cm.)

Now introduce the second type of Uniform-Motion Problem, "If the two cars are 
750 cms apart and they each travel towards each other at the same time, when and
where will the two cars meet?".  Set the cars on opposite sides of the room and
let them run into each other as you begin your explanation.  Again use the 
standard associated pictures and charts for this type of problem, write the 

equation and solve it in the usual manner.

                              25t + 36t = 750         (12.29)(25) = 307.25 cm
                                    61t = 750
                                      t = 12.29

They should collide in approximately 12 secs, 307 cm from where the slower car 
starts.  Mark that spot on the floor.  Place the cars 750 cms apart and run them
at each other.   (I missed by 6 cm.) 
 
Performance Assessment:

     With two faster cars mark the starting and finishing lines for calculating 
the velocity over a fixed distance.  (I used 20 yards.)  Also mark two starting 
lines on opposite ends of the hallway.  (65 yards)  In teams of 3 or 4, the 
students find the velocities, make the associated picture and chart, write the 
equation and solve it in the usual manner, and mark the spot in the hall where 
the two cars will collide.  (This is competition at its best.)