The motion is given by the equation of the coordinate x (t) = 2 + 3t + 0.4t ^2 determine

The motion is given by the equation of the coordinate x (t) = 2 + 3t + 0.4t ^2 determine: 1.the initial coordinate of the body 2.projection of the body’s velocity 3.projection of acceleration 4.the type of motion 5.write the equation of the projection of speed 6.determine the value of the coordinate and speed at time t = 6 s

x (t) = 2 + 3 * t + 0.4 * t ^ 2.

t = 6 s.

x0 -?

V0х -?

Vx (t) -?

x -?

The dependence of the coordinate of the body at uniformly accelerated motion has the form: x (t) = x0 + V0x * t + ax * t2, where x0 is the coordinate of the body at the beginning of movement, V0x is the projection of the initial velocity, and ax is the projection of acceleration.

Since our dependence has the form x (t) = 2 + 3 * t + 0.4 * t2, the body moves uniformly accelerated from the initial coordinate x0 = 2 m, the projection of the initial velocity is V0x = 3 m / s, the projection of acceleration is ax = 0.8 m / s2.

When the body moves with constant acceleration: Vx (t) = V0x + ax * t.

Vx (t) = 3 + 0.8 * t.

Vx = 3 + 0.8 * 6 = 7.8 m / s.

x = 2 + 3 * 6 + 0.4 * (6) 2 = 34.4 m.

Answer: x0 = 2 m, V0x = 3 m / s, Vx (t) = 3 + 0.8 * t, Vx = 7.8 m / s, x = 34.4 m.