A fireworks shell is accelerated from rest to a velocity of 82.0 m/s over a distance of 0.400 m. (a) How long did the acceleration last

Find the acceleration:

v² - u² = 2ax

(v = final velocity, u = initial velocity, a = acceleration, x = displacement)

(82.0 m/s)² - 0² = 2 a (0.400 m)

a = (82.0 m/s)² / (2 (0.400 m))

a = 8405 m/s²

Find the time:

x = ut + 1/2 at²

(t = time)

0.400 m = 0 + 1/2 (8405 m/s²) t²

t² = (0.400 m) / (1/2 (8405 m/s²))

t = √((0.400 m) / (1/2 (8405 m/s²)))

t ≈ 0.00976 s

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