# Using the formula for the dependence of the coordinates of the body on time (equation of motion), determine the initial position

**Using the formula for the dependence of the coordinates of the body on time (equation of motion), determine the initial position and speed of the body (km.h). What path will he cover in 10 hours? y = 6 + 6t**

Given:

y = 6 + 6 * t – the equation of body motion;

t = 10 hours – time interval.

It is required to determine the initial position of the body y0 (kilometer), the velocity of the body v (kilometer per hour) and the path that the body will cover in a time interval equal to t.

Determine the initial position of the body by substituting the value t = 0 into the equation of body motion:

y = 6 + 6 * t = 6 + 6 * 0 = 6 + 0 = 6 kilometers.

To find the speed, it is necessary to perform the first-degree derivative of the equation of motion of the body:

v = y (t) ‘= (6 + 6 * t)’ = 6 kilometers per hour.

Then:

S = v * t = 6 * 10 = 60 kilometers.

Answer: the initial coordinate of the body is 6 kilometers, the speed of the body is 6 km / h, the distance traveled is 60 kilometers.