Question

ПОМОГИТЕ! Найдите мгновенную скорость точки движущейся прямолинейно по закону х(t) в момент времени t0 если t^2-2t, t0 = 3

Answer 1

Ответ: 4

Пошаговое объяснение:

V(t)=X'(t)=2t-2,  V(2)=2*3-2=4

Answer 2

Understanding the problem

You are looking to find the instantaneous velocity of a point moving along a straight line according to the equation x(t), at a specific moment in time t0. The equation x(t) is given as t^2 - 2t, and t0 is given as 3.

Solution

To find the instantaneous velocity at a specific moment in time, we need to find the derivative of the position function x(t) with respect to time t. The derivative of x(t) represents the rate of change of the position with respect to time, which is the velocity.

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

x(t) = t^2 - 2t

To find the derivative, we can apply the power rule of differentiation. According to the power rule, if we have a function of the form f(t) = t^n, then the derivative of f(t) with respect to t is given by:

f'(t) = n * t^(n-1)

Applying the power rule to x(t) = t^2 - 2t:

x'(t) = (2t^1) - (2 * 1 * t^(1-1)) = 2t - 2

Now we have the derivative of x(t) with respect to t, which represents the instantaneous velocity of the point. To find the instantaneous velocity at the specific moment in time t0, we substitute t0 into the derivative expression:

x'(t0) = 2 * t0 - 2

Substituting t0 = 3:

x'(3) = 2 * 3 - 2 = 6 - 2 = 4

Therefore, the instantaneous velocity of the point at t0 = 3 is 4 units per time (e.g., meters per second, kilometers per hour, etc.).