The movement of a point is given by the equation x = 4 + 5t + 2t ^ 2. Determine the starting coordinate

The movement of a point is given by the equation x = 4 + 5t + 2t ^ 2. Determine the starting coordinate of the movement, starting speed and acceleration. What is the displacement of the body 5 s after the start of the movement?

Given:

x = 4 + 5 * t + 2 * t ^ 2 – the equation of body motion;

t = 5 seconds.

It is required to find the initial coordinate X0, the initial velocity V0, the acceleration of the body a and the displacement of the body through time t.

The general equation of body motion is:

x (t) = X0 + V0 * t + a * t ^ 2 / 2. Substituting the known values ​​from our equation, we get:

Initial coordinate X0 = 4 m;

Initial speed V0 = 5 m / s;

The acceleration of the body is a = 4 m / s ^ 2.

Let’s calculate the displacement:

S = 4 + 5 * t + 2 * t ^ 2 = 4 + 5 * 5 + 2 * 5 ^ 2 = 4 + 25 + 50 = 79 meters.

Answer: the initial coordinate is X0 = 4 m, the initial velocity is V0 = 5 m / s, the acceleration of the body is a = 4 m / s ^ 2, the movement of the body in 5 seconds is 79 meters.