With what acceleration does the body move without initial velocity, if in 4 s after the beginning

With what acceleration does the body move without initial velocity, if in 4 s after the beginning of the movement it has passed the path of 16 m? Determine the path covered in 6 seconds.

1) The distance traveled with uniformly accelerated motion can be found by the formula: S = vo • t + (a • t ^ 2): 2, where vo is the initial velocity of the body, a is the acceleration, t is the time. If the body moves without initial velocity, then vo = 0 m / s, we obtain an abbreviated version of the formula: S = (a • t ^ 2): 2. According to the problem statement, the body, 4 s after the start of motion, traveled a distance of 16 m to find the acceleration , we will express it from the formula of the traversed path: a = 2S: (t ^ 2). Let’s substitute the values of physical quantities and make a calculation. a = 2 • (16m): (4s • 4s) = 2 m / (s • s).
2) In t = 6 s, the body will pass S = (2 • 36): 2 = 36 (m).
Answer: 2 m / (s • s); 36 m.