The equation of motion for a body weighing 2 kg has the form x = 3 + 2t + 1t ^ 2.

The equation of motion for a body weighing 2 kg has the form x = 3 + 2t + 1t ^ 2. The kinetic energy of the body in time t = 1c is equal to?

The equation of motion for a body weighing 2 kg has the form x = 3 + 2t + 1t ^ 2. The kinetic energy of the body in time t = 1c is equal to? I beg you with an explanation of how we consider the equation

x = 3 + 2 * t + 1 * t ^ 2.

m = 2 kg.

t = 1 s.

Ek -?

1 way.
When moving with constant acceleration, the coordinate of the body is expressed by the dependence: x = x0 + V0 * t + a * t ^ 2/2, where x0 is the initial coordinate of the body, V0 is the initial velocity of the body, t is the time of movement, + a is the acceleration of motion.

x0 = 3 m, V0 = 2 m / s, a = 2 m / s ^ 2.

The body speed is determined by the relationship: V = V0 + a * t.

V (1) = 2 + 2 * 1 = 4 m / s.

Let’s find the kinetic energy by the formula: Ek = m * V ^ 2/2.

Ek = 2 kg * (4 m / s) ^ 2/2 = 16 J.

Method 2.
The kinetic energy is determined by the formula: Ek = m * V ^ 2/2.

The speed of a body is a derivative of its coordinate: V (t) = x (t) *.

V (t) = x (t) * = 2 +1 * 2 * t.

V (1) = 2 + 1 * 2 * 1 = 4 m / s.

Ek = 2 kg * (4 m / s) ^ 2/2 = 16 J.

Answer: Ek = 16 J.