Question

Unreasonable results Dragsters can actually reach a top speed of 145.0 m/s in only 4.45 s. (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 402.0 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) 278 m/s; (c) The acceleration increases over time due to more force.
b) (a) 35.0 m/s²; (b) 348 m/s; (c) The acceleration decreases over time due to less force.
c) (a) 45.0 m/s²; (b) 400 m/s; (c) The acceleration remains constant, leading to a higher final velocity.
d) (a) 29.1 m/s²; (b) 247 m/s; (c) The acceleration fluctuates randomly, leading to a higher final velocity.

Answer 1

The average acceleration of the dragster is 32.6 m/s², derived from its top speed and time taken. However, the final velocity calculation based on constant acceleration is inaccurate, as dragsters have greater acceleration at the start which decreases over time, affecting the final velocity.

Step-by-step explanation:

To address the student's physics problem, we will calculate the average acceleration of a dragster, find the final velocity over a quarter-mile distance, and discuss the plausibility of constant acceleration in this scenario.

(a) Calculating Average Acceleration

The average acceleration a can be found using the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the time taken. The dragster reaches a top speed (final velocity) of 145 m/s from rest (initial velocity 0 m/s) in 4.45 s, so Δv is 145 m/s. The average acceleration is thus 145 m/s divided by 4.45 s, which equals 32.6 m/s².

(b) Finding Final Velocity Over a Quarter Mile

To find the final velocity (v) without the time information, we use the kinematic equation v² = u² + 2as, where u is the initial velocity, a is the acceleration calculated in part (a), and s is the distance. Substituting the given values, u = 0 m/s, a = 32.6 m/s², and s = 402 m, we find that v² = 0 + 2 * 32.6 m/s² * 402 m. Solving for v gives a final velocity greater than 145 m/s. This discrepancy hints that the assumption made in the calculation may be incorrect, as it assumes constant acceleration.

(c) Discussing the Validity of Constant Acceleration

Acceleration in dragsters is not usually constant. Dragsters often have greater acceleration at the start of the race due to lower initial speeds and higher power application, and acceleration decreases as speed increases. Therefore, if acceleration decreases over time, the dragster would not be accelerating at 32.6 m/s² toward the end of the run, and the final velocity should be less than calculated if constant acceleration was assumed.