# The car, moving in a straight line, drove a path of 10 meters, then made a turn, circumscribing a quarter

**The car, moving in a straight line, drove a path of 10 meters, then made a turn, circumscribing a quarter circle with a radius of 10 meters, and drove further along a straight line for 10 meters. Determine the path traveled by him and the module of movement.**

S1 = 10 m.

n = 1/4.

R = 10 m.

S2 = 10 m.

L -?

S -?

By the movement of the body L is called the length of the line that the body describes during movement. When moving, the body passed two straight sections with a length of S1 = 10 m, S2 = 10 m and 1/4 of the circumference of a circle with a radius R.

L = S1 + S2 + n * 2 * P * R.

L = 10 m + 10 m + 2 * 3.14 * 10 m / 4 = 35.7 m.

The movement of the body S is a vector that connects the initial and final position of the body. The movement of the car S will be the hypotenuse of a right-angled triangle with legs S1 + R and S2 + R.

By the Pythagorean theorem: S = √ ((S1 + R) ^ 2 + (S2 + R) ^ 2).

S = √ ((10m + 10m) ^ 2 + (10m + 10m) ^ 2) = 28.28m.

Answer: vehicle path L = 35.7 m, displacement S = 28.28 m.