The body at rest begins to move with constant acceleration. In the third second, it travels a path of 10 m

The body at rest begins to move with constant acceleration. In the third second, it travels a path of 10 m. What path does the body cover in 8 seconds?

Given: S (3) (path covered in the third second) = 10 m; t (duration of movement) = 8 s; uniformly accelerated motion from a state of rest.

1) Determine the constant acceleration: S (3) = S3 – S2 = 0.5 * a * t3 ^ 2 – 0.5 * a * t2 ^ 2 = a * (0.5t3 ^ 2 – 0.5t2 ^ 2) , whence a = S (3) / (0.5t3 ^ 2 – 0.5t2 ^ 2) = 10 / (0.5 * 3 ^ 2 – 0.5 * 2 ^ 2) = 4 m / s2.

2) Calculate the path covered in 8 s: S8 = 0.5 * a * t8 ^ 2 = 0.5 * 4 * 8 ^ 2 = 128 m.

Answer: 3) in 8 seconds the body will cover a path of 128 m.