In the third second of uniformly accelerated motion with zero initial velocity, the body traverses a path 35 m long.

In the third second of uniformly accelerated motion with zero initial velocity, the body traverses a path 35 m long. Find the length of the path in the first 8 s of motion.

Initial data: S (3) (the path that the body covered in the third second of movement) = 35 m; V0 (initial velocity of the body) = 0 m / s; t (movement time) = 8 s; a = const, since the motion is uniformly accelerated.

1) Let’s calculate the acceleration of the body:

S (3) = S3 – S2 = a * t3 ^ 2/2 – a * t2 ^ 2/2 = 1/2 a * (3 ^ 2 – 2 ^ 2) = 1/2 a * (9 – 4) = 2.5a.

a = S (3) / 2.5 = 35 / 2.5 = 14 m / s ^ 2.

2) Determine the path length in 8 s:

S = a * t ^ 2/2 = 14 * 8 ^ 2/2 = 448 m.

Answer: The length of the path for the first 8 seconds of movement is 448 meters.