Question

Dragsters can actually reach a top speed of 145 m/s in only 4.45 s—considerably less time than given in Example 2.10 and Example 2.11. (a) Calculate the average acceleration for such a dragster. (b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for 402 m (a quarter mile) without using any information on time. (c) Why is the final velocity greater than that used to find the average acceleration? Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity.

(a)(a) 32.6 m/s²; (b) 145 m/s; (c) The acceleration is greater at the beginning.

(b)(a) 25.8 m/s²; (b) 115 m/s; (c) The acceleration is greater at the end.

(c)(a) 28.1 m/s²; (b) 130 m/s; (c) The acceleration is constant throughout.

(d)(a) 30.0 m/s²; (b) 140 m/s; (c) The acceleration decreases over time.

Answer 1

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.