The car starts accelerating from standstill along a long straight track.

The car starts accelerating from standstill along a long straight track. In what second of acceleration will it cover a distance 9 times greater than in the first second?

Since it drives uniformly accelerated, the path formula:
S = ((a * t ^ 2) / 2) + V0 * t, where S is the distance traveled (m), a = g is the acceleration of the car (m / s ^ 2), t is the time the car is moving (s), V0 – initial vehicle speed (V = 0).
Then:
S = ((a * t ^ 2) / 2) + V0 * t = (a * t ^ 2) / 2.
From the initial conditions: S2 = 9S1, where S1 is the distance covered in 1 s of acceleration.
S1 = (a * t1 ^ 2) / 2 = 0.5a.
S2 = (a * t2 ^ 2) / 2.
9S1 = (a * t2 ^ 2) / 2.
9 * 0.5a = (a * t2 ^ 2) / 2.
t2 ^ 2 = 9.
t2 = √9 = 3.
Answer: The car will cover the required distance in 3 seconds of acceleration.