# Bumper Car Rally

## by Tom Deets

Tom is a full-time high school physics teacher and a graduate student in Educational Technology.

Instructional Objective The learners will be able to calculate distances achieved by an object after they have been given an initial velocity, an acceleration and a time period. They will also be able to distinguish between initial and final velocities and be able to utilize these concepts in problem-solving situations involving sequential times. The learners will see how an elastic collision effects the movement of the objects involved. Finally the learners will grasp the concept of inertia.

Learners/Context The learners are students in an introductory physics class.

The game is designed to be played during or after a instructional unit dealing with motion. This game could also be used during a unit considering Newton's laws, primarily the law of inertia. It could also be used during a unit involving momentum and its conservation and elastic and inelastic collisions.

Rationale A game is an appropriate format for this situation because it helps to simulate what would be impossible and dangerous within an ordinary classroom. It also makes what could potentially be dry material fun.

Rules Bumper Car Rally Game Rules

The objective of the game is to be the first player to reach the opposite side of the game board.

1. Before the game begins each player should place their game token on one of the four start positions. Each player should then spin the acceleration spinner. The player who gets the greatest number goes first. Play should then proceed clockwise with respect to this player.

2. The first player should spin the time spinner and then the acceleration spinner. If either of these is a zero their turn is over and it is the next persons turn to go.

3. When a player succeeds in achieving non-zero values from both spinners they can calculate the displacement achieved by their game piece by using the paper acceleration calculator. By sliding the center piece until both their acceleration and time are visible they will see their displacement. They should then move their game piece forward that number of spaces (unless they have achieved negative displacement, in which case they will move backward).

4. The player can then calculate their change in velocity (which will become their initial velocity for their second turn) by using the paper velocity calculator. This calculator works the same as the acceleration calculator except that it calculates your change in velocity rather than accelerated displacement. At the end of each turn the player should determine what their final velocity is by adding the change in velocity (which could be negative) to their initial velocity for that turn. Each player should keep track of their velocity at all times throughout the game.

5. When a game player has a non-zero initial velocity they will have to add (or subtract) additional displacement, depending on the value of their current initial velocity. The final velocity achieved at the end of the previous turn is now the initial velocity for the current turn.

To calculate the additional displacement (whether positive or negative) the game player needs to multiply their current initial velocity by the time received by the time spinner. For the total displacement achieved the player will add this additional displacement to the accelerated displacement displayed on the paper acceleration calculator. If either or both of these quantities is negative it is possible to receive a negative net displacement, in which case the game piece will have to be moved backwards.

When a player receives a zero for acceleration and a non-zero time they will still move their piece due to their initial velocity for that turn (inertia).

When a player lands on a Road Conditions space they will take the top card from the deck of cards provided. Whatever the instructions turn out to be the player will follow the instructions accordingly and then place this card at the bottom of the deck. The exceptions to this are as follows:

¥ Monkey Wrench Cards: This card can be kept by the player to be dealt to an opponent at any time during the course of the game. When dealt the card should be given to the player immediately after they have received their acceleration from the spinner. Note; a player who receives an acceleration of - 2 cannot be decelerated anymore than this.

¥ Time Flies and Super Fuel Cards: When these cards are received they should be used during the very next turn. However, time acquired can never exceed two seconds and the acceleration can never exceed + 4.

Intersections

If a player lands on an intersection space they are susceptible to collisions with opposing players. If another player reaches the intersection while it is already inhabited by a game piece, the player who was moving must stop at the intersection and the original inhabitant gets pushed in the direction that the moving player was moving before the collision.

The number of spaces that the playing piece gets moved during the collision can be calculated by multiplying what would have been the final velocity for the player who had been moving by the number of seconds received from the time spinner for that turn. This final velocity is now the initial velocity for the hit piece and the piece that had been moving originally receives a zero final velocity.

The player who was struck in the intersection must now proceed in the direction indicated by the arrows on the playing board.

Rear-End Collisions

If a game piece overtakes another playing piece from behind they must stop on the space occupied by the other piece. Their final velocity is then zero for that turn.

The "hit" piece then moves forward the number of spaces calculated using the same techniques outlined under Intersections above.

The game is played in the following manner: After determining who goes first the players take turns going clockwise around the game board. When it is their turn each player should spin both of the spinners. If the time spinner delivers a zero then that players turn is over. However, if the acceleration delivers a zero the player may get to move if they have a non-zero initial velocity. This helps to demonstrate the concept of inertia. The end objective is to reach the other side of the game board first. This objective could be amended so that the player has to return to their starting position, or they could even be required to complete several laps of the game board. Another option that could help slow the play down would be to impose a "speed" limit. Otherwise it is possible to generate incredible speeds resulting in enormous displacements.

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Card Design

Each game card used with the game has a border with simplified instructions. The only cards with any complexity are the Monkey Wrench cards, the Super Fuel cards and the. The detailed instructions for these cards are included in the instructions above.

Board Design

The game board eventually evolved into a clover-leaf shape. This allowed for intersections as well as a cyclical format.

Design Process I started by considering this idea as a card game. It became obvious that the complexity of the physics concepts represented would be better served in a board game format. The evolving shape of the game board suggested other conceptual possibilities such as one and two dimensional elastic collisions.

References Murphy, Zitzewitz, Physics, it's Principles and Problems, Merril, NY, Copyright 1989

Last updated by Tom Deets> on October 19, 1995.