Question

Точка движется по закону x(t)= корень из t. Найдите её скорость в момент времени 4с? Полное решение пожалуйста

Answer 1

Ответ:

0,25 м/с

Пошаговое объяснение:

$X(t)=\sqrt{x}$

Мгновенная скорость равна производной перемещения по времени, а именно:

$V(t)=X`(t)=(\sqrt{x} )`=\frac{1}{2\sqrt{x}}$

Находим скорость точки в момент времени t=4 c

$V(4)=\frac{1}{2\sqrt{4}}=\frac{1}{2*2}=\frac{1}{4}=0,25$  (м/с)

Answer 2

Problem Analysis

We are given that the position of a point is given by the function x(t) = √t. We need to find the velocity of the point at t = 4s.

Solution

To find the velocity of the point, we need to take the derivative of the position function x(t) with respect to time t.

Let's find the derivative of x(t) = √t with respect to t:

d/dt (x(t)) = d/dt (√t)

To find the derivative of √t, we can use the power rule of differentiation:

d/dt (√t) = (1/2) * t^(-1/2)

Now, let's substitute t = 4 into the derivative to find the velocity at t = 4s:

v(4) = (1/2) * 4^(-1/2)

Simplifying the expression:

v(4) = (1/2) * 2^(-1/2)

v(4) = (1/2) * √(1/2)

Therefore, the velocity of the point at t = 4s is (1/2) * √(1/2).

Answer

The velocity of the point at t = 4s is (1/2) * √(1/2).