Find the displacement of a body in the 7th second if it moved from a state of rest with an acceleration of 2 m / s ^ 2

t1 = 6 s.

t2 = 7 s.

V0 = 0 m / s.

a = 2 m / s2.

S7 -?

To find the movement of the body in the seventh second S7, it is necessary to subtract the movement of the body in six seconds S1 from the movement of the body in seven seconds S2: S7 = S2 – S1.

Since the body moves early with acceleration with acceleration a, its movement is determined by the formula: S = V0 * t + a * t2 / 2, where V0 is the initial velocity of the body, t is the time of its movement.

Since the body moved from a state of rest V0 = 0 m / s, the formula will take the form: S = a * t ^ 2/2.

S1 = a * t1 ^ 2/2.

S1 = 2 m / s2 * (6 s) ^ 2/2 = 36 m.

S2 = a * t2 ^ 2/2.

S2 = 2 m / s2 * (7 s) ^ 2/2 = 49 m.

S7 = 49 m – 36 m = 13 m.

Answer: the body in the seventh second of its movement made a displacement of S7 = 13 m.