Final answer:
Joe is mistaken in his assumption; increasing the distance over which he measures his toy car's acceleration would not affect the measurement provided the acceleration remains constant. It would simply allow for a more accurate measurement of time. Just as in the reaction time experiment with gravity, a longer distance allows a more precise evaluation of constant acceleration over time.
Step-by-step explanation:
Joe's assumption that changing the distance would change the measurement of the acceleration is incorrect, provided that the car's propulsion system continues to work at full power and the car's acceleration doesn't change due to other factors. In simple terms, acceleration is defined as the change in velocity over the change in time. As long as Joe's toy rocket-powered car is accelerating at a constant rate and has not reached its top speed, the acceleration can be calculated over any distance. Increasing the distance simply allows for a more accurate measurement of time, which could indeed be too short to measure over shorter distances. It's like calculating reaction time with a ruler in the take-home experiment; the distance the ruler falls allows for an accurate measurement of the time it takes for a person to react, which relates to the constant acceleration due to gravity that acts on the ruler.
For example, if the car's acceleration was meant to be constant, then regardless of whether the distance is 0.500 m or a greater distance like 2.00 m, the average acceleration should remain the same. Joe needs to measure the time it takes for the car to travel that specified distance and then apply the formula for average acceleration, which is the change in velocity (final velocity minus initial velocity) divided by the change in time.