A body weighing 4 kg moves rectilinearly according to the law S = 1 + t + t ^ 2 (m / s). Find its kinetic energy for 5 sec.

To find the kinetic energy of a body at 5 seconds of motion, we apply the formula: Ek = m * V ^ 2/2 = m * (S (t) ‘) ^ 2/2.

Variables and functions: m – body weight (m = 4 kg); the law of motion S (t) = 1 + t + t ^ 2; t – considered time (t = 5 s).

Calculation: Ek = m * (S (t) ‘) ^ 2/2 = 4 * ((1 + t + t ^ 2)’) ^ 2/2 = 4 * (0 + 1 + 2t) ^ 2/2 = 4 * (1 + 2 * 5) ^ 2/2 = 4 * 112/2 = 242 J.

Answer: After 5 seconds of movement, the kinetic energy of the body will be equal to 242 J.