A body weighing 1 kg under the action of a constant force moves in a straight line. The dependence of the

A body weighing 1 kg under the action of a constant force moves in a straight line. The dependence of the coordinates of the body on time is expressed by the equation X = 2t ^ 2-3t ^ 2 + 1. Determine the work in the first 5 seconds of force action.

To calculate the work of an acting constant force, we use the formula: A = F * S = m * a * x (t) = m * x (t) ” * x (t).

Variables and functions: m – body weight (m = 1 kg); the equation of motion x (t) = 2t ^ 2 – 3t + 1; t – elapsed time (t = 5 s).

Calculation: A = m * x (t) ” * x (t) = 1 * (2t ^ 2 – 3t + 1) ” * (2t ^ 2 – 3t + 1) = 1 * 4 * (2 * 5 ^ 2 – 3 * 5 + 1) = 144 J.

Answer: In the first 5 seconds, the acting constant force performed work of 144 J.