"In a drag race a car starts at rest and attempts to cover 440 yd in the shortest possible time. The world record is 5.637s; the final speed was 250.69 mi/h at the 440 yd mark"
a)What was the average acceleration?
b)Prove that the car did not move with constant acceleration
c)What would have been the final speed if the car had moved with constant acceleration so as to reach 440 yd in 5.637 s?
V_initial: 0 ft/s V_final: 367.68 ft/s T: 5.637 s Distance: 1320 ft
For a) avg a = ΔV / Δt
for b) constant a = (V_initial + V_final) / 2
for c) V_final = V_initial + a_constant * time
The Attempt at a Solution
a) Avg a = 65.23 ft/s^2 No problems here
b) Using the constant acceleration equation above (which I am somewhat dubious of), a_constant = 183.84 ft / s^2. Intuitively, I believe that the average acceleration would have to be equal to the constant acceleration if this was indeed a case of constant acceleration. I'm not quite sure i can defend that logically.
c) Using the constant acceleration calculated above, V_final = 1036 ft/s, which is clearly way too high (V_final was given as 367.68 ft/s). So I think perhaps this high velocity answer proves part b.
How do I logically explain part b? Am I correct in using the constant acceleration equation described above? Or is there a totally different way to address this problem?