The rectilinear motion of the body is described by the equation x = 6 + 8t – 2t2.

The rectilinear motion of the body is described by the equation x = 6 + 8t – 2t2. Find the path covered by the body in 3 seconds of movement.

If a rectilinear body is described by a quadratic equation in time, then this is uniformly accelerated motion. Since the free term of the equation is not zero, the motion began from a point equal to the free term (projection onto the x axis). The time is set in seconds, so the distance is in meters.

So, the movement at the moment t = 0 began from the point 6m:

x = 6 + 8 * 0 – 2 * t ^ 2.

3 seconds have passed, by this moment the body is at the point x1:

x1 = 6 + 8 * 3 – 2 * 3 ^ 2;

x1 = 6 + 24 – 2 * 9;

x1 = 30 – 18;

x1 = 12.

The starting point from which the movement began is 6m, which means that the body has passed 6 meters in 3 seconds.

Answer: in 3 seconds, the body has traveled 6 meters.