Final answer:
The average acceleration of the dragster is 32.6 m/s², and the final velocity, starting from rest and accelerating at this rate for 402 m, is 145 m/s. The final velocity can be greater than the average acceleration because the dragster changes gears and the acceleration is higher at the beginning of the run.
Step-by-step explanation:
(a) To calculate the average acceleration of the dragster, we can use the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Since the dragster starts from rest and reaches a final velocity of 145 m/s in 4.45 s, the average acceleration is:
Acceleration = (145 m/s - 0 m/s) / 4.45 s = 32.6 m/s²
(b) To find the final velocity of the dragster starting from rest and accelerating at the rate found in (a) for 402 m, we can use the formula:
Final Velocity² = Initial Velocity² + 2 * Acceleration * Displacement
Since the dragster starts from rest, the initial velocity is 0 m/s. Plugging in the values, we get:
Final Velocity² = 0 m/s + 2 * 32.6 m/s² * 402 m
Solving for the final velocity, we get:
Final Velocity = sqrt(2 * 32.6 m/s² * 402 m) = 145 m/s
(c) The assumption of constant acceleration is not valid for a dragster because it changes gears. The acceleration would be greater at the beginning of the run when the dragster is in first gear, and would decrease as it shifts into higher gears.
This means that the average acceleration we calculated is an average over the entire run and does not represent the acceleration at the end. Therefore, the final velocity can be greater than the average acceleration.