When moving along the x-axis, the coordinate of the body changes according to the law x = (2 + 3t) where t is the time

When moving along the x-axis, the coordinate of the body changes according to the law x = (2 + 3t) where t is the time in seconds. What path does the body cover in 3 seconds of movement?

Given:

x (t) = 2 + 3 * t – the equation of body motion;

t = 3 seconds – time span.

It is required to determine the path S that the body will pass during the time interval t.

Let’s find the coordinate in which the body was at the initial moment of time:

x (0) = 2 + 3 * t = 2 + 3 * 0 = 2 meters.

Let us find the coordinate in which the body was at the moment t:

x (t) = 2 + 3 * t = 2 + 3 * 3 = 2 + 9 = 11 meters.

Then the traversed path will be equal to:

S = x (t) – x (0) = 11 – 2 = 9 meters.

Answer: the body has traveled a distance of 9 meters.