The car is moving along the road. The time dependence of the speed is described by the equation

The car is moving along the road. The time dependence of the speed is described by the equation V = 2 + t. Determine the path traveled by the car in 1 minute.

V (t) = 2 + t.

t = 1 min = 60 s.

S -?

With uniformly accelerated motion, the speed of the body V (t) changes according to the formula: V (t) = V0 + a * t, where V0 is the initial speed of the body, and is the acceleration during motion.

For the dependence V (t) = 2 + t, the initial velocity is V0 = 2 m / s, the acceleration of the body is a = 1 m / s2.

The path of the body at uniformly accelerated motion is determined by the formula: S = x – x0, where x is the coordinate of the body at time t, x0 is the initial coordinate of the body.

x (t) = x0 + V0 * t + a * t ^ 2/2.

S = x0 + V0 * t + a * t ^ 2/2 – x0 = V0 * t + a * t ^ 2/2.

S = 2 * t + t ^ 2/2.

S = 2 * 60 s + 1 m / s2 * (60 s) ^ 2/2 = 1920 m.

Answer: the car has traveled the path S = 1920 m.