The body, moving uniformly accelerated and at rest, passes 7 meters in the fourth second from

The body, moving uniformly accelerated and at rest, passes 7 meters in the fourth second from the beginning of the movement. What path will the body take in 10 seconds? What speed will it reach at the end of the tenth second?

t1 = 3 s.

t2 = 4 s.

S4 = 7 m.

t = 10 s.

V0 = 0 m / s.

S -?

V -?

Let us express the path of the body S1 during the movement t1 = 3 s.

S1 = V0 * t1 + a * t1 ^ 2/2, where a is the acceleration of the body. Since the initial velocity of the body is V0 = 0 m / s, the formula will take the form: S1 = a * t1 ^ 2/2.

Let us express the path of the body S2 during the movement time t2 = 4 s.

S2 = V0 * t2 + a * t2 ^ 2/2. Since the initial velocity of the body is V0 = 0 m / s, the formula will take the form: S2 = a * t2 ^ 2/2.

S4 = S2 – S1 = a * t2 ^ 2/2 – a * t1 ^ 2/2 = = a * (t2 ^ 2/2 – t1 ^ 2) / 2.

Let us express the acceleration of the body: a = 2 * S4 / (t2 ^ 2 – t1 ^ 2).

a = 2 * 7 m / ((4 s) ^ 2 – (3 s) ^ 2) = 2 m / s ^ 2.

S = a * t ^ 2/2.

S = 2 m / s ^ 2 * (10 s) ^ 2/2 = 100 m.

V = a * t.

V = 2 m / s ^ 2 * 10 s = 20 m / s.

Answer: S = 100 m, V = 20 m / s.