The body moves according to the law S (t) = x ^ 2-4x + 3. Determine what moment in time the speed will be equal to 4.

S (t) = x ^ 2 – 4 * x + 3.

1 way.

The equation for the dependence of the distance traveled on time for motion with constant acceleration has the form:

S (t) = S0 + V0 * x + a * x ^ 2/2, where V0 is the initial speed of movement, and is the acceleration of movement.

S0 = 3, V0 = -4, a = 2.

The dependence of the speed has the form: V = V0 + a * x.

V = – 4 + 2 * x.

x = (V + 4) / 2.

By condition, V = 4, x = (4 + 4) / 2 = 4.

Method 2.

The speed of movement V (t) is the derivative of the movement S (t) “.

S (t) = x ^ 2 – 4 * x + 3.

V (t) = S (t) “= (x ^ 2 – 4 * x + 3)” = 2 * x – 4.

x = (V (t) + 4) / 2.

x = (4 + 4) / 2 = 4.

Answer: the speed V = 4 will be in time x = (4 + 4) / 2 = 4.