The movement of the body is given by the equation x = 0.5 + 2t + 5t ^ 2 (m). Determine the path traveled

The movement of the body is given by the equation x = 0.5 + 2t + 5t ^ 2 (m). Determine the path traveled in a time interval of 10 s.

x (t) = 0.5 + 2 * t + 5 * t ^ 2.

t = 10 s.

S -?

With uniformly accelerated motion, the coordinate of the body changes according to the law: x (t) = x0 + V0 * t + a * t ^ 2/2, where x0 is the initial coordinate of the body, V0 is the initial speed of motion, a is the acceleration of motion.

x0 = 0.5, V0 = 2 m / s, a = 10 m / s2.

Since the body moves along one coordinate axis, the path S traversed by the body will be determined by the formula: S = x (t) – x0.

x (10 s) = 0.5 + 2 * 10 + 5 * (10) ^ 2 = 520.5 m.

S = 520.5 m – 0.5 m = 520 m.

Answer: the body has passed the path S = 520 m.