Final answer:
To find the sled's position between t=4.0s and t=9.0s, substitute the values of a, b, and c into the position formula. To find the average speed, calculate the total distance traveled and divide by the time taken.
Step-by-step explanation:
To find the sled's position between t=4.0s and t=9.0s, we substitute the values of a, b, and c into the position formula. Given a = 2.0 m/s^2, b = 2.0 m/s^3, and c = 3.0 m, the position formula becomes x = 2.0 + 2.0t + 3.0. Substituting t = 4.0s and t = 9.0s into the formula, we get x = 2.0 + 2.0(4.0) + 3.0 and x = 2.0 + 2.0(9.0) + 3.0. Evaluating these expressions gives us the sled's position between the given time intervals.
To find the average speed between t=4.0s and t=9.0s, we calculate the total distance traveled by the sled during this time interval. Using the position formula x = 2.0 + 2.0t + 3.0, we find the sled's positions at t=4.0s and t=9.0s. The average speed is then calculated by dividing the total distance traveled by the time taken.