# An equation is given for the movement of a body: x = 20t-t ^ 2 Define: a) how does the body move

**An equation is given for the movement of a body: x = 20t-t ^ 2 Define: a) how does the body move: in a straight line x or against? B) its initial coordinate x0 B) the projection of the initial velocity on the x-axis v0x D) the projection of the acceleration on the x-axis ax E) the type of motion E) write down the equation of speed**

x (t) = 20 * t – t ^ 2.

x0 -?

V0x -?

ah -?

Vx (t) -?

With uniformly accelerated motion with an initial speed V0, acceleration a and an initial coordinate x0, the dependence of the coordinate on time x (t) has the form: x (t) = x0 + V0x * t + ax * t ^ 2/2.

For our dependence x (t) = 20 * t – t2, we see that the body moves from the initial coordinate x0 = 0 m, the projection with the initial velocity V0x = 20 m / s, acceleration ax = – 2 m / s2.

Since V0х = 20 m / s> 0, the body moves in the direction of the ox axis. But if ax = – 2 m / s2 <0, then the body is inhibited.

With uniformly accelerated motion, the speed of the body changes according to the formula: Vx (t) = V0x + ax * t.

For our movement, the dependence will have the form: Vх (t) = 20 – 2 * t.

Answer: x0 = 0 m, V0x = 20 m / s, ax = – 2 m / s2, Vx (t) = 20 – 2 * t.