A material point with a mass of 3 kg moves rectilinearly according to the law x (t) = 3-2t + t ^ 2
| September 19, 2021 | education
A material point with a mass of 3 kg moves rectilinearly according to the law x (t) = 3-2t + t ^ 2 find the kinetic energy at the moment t = 4.
m = 3 kg.
x (t) = 3 – 2 * t + t ^ 2.
t = 4 s.
Ek -?
The kinetic energy of a material point Ek is determined by the formula: Ek = m * V ^ 2/2, where m is the mass of the material point, V is the speed of movement.
The dependence of the speed of movement of the body V (t) is the derivative of the dependence of its coordinate x (t) “: V (t) = x (t)”.
V (t) = (3 – 2 * t + t ^ 2) “= -2 + 2 * t.
V (4 s) = -2 + 2 * 4 = 6 m / s.
Substitute the data into the formula for kinetic energy: Ek = 3 kg * (6 m / s) ^ 2/2 = 54 J.
Answer: the material point has kinetic energy Ek = 54 J.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
