Question

X=2t +0,2t² написати залежність v=v(t) ​

Answer 1

Ответ:

Объяснение:

X=2t +0,2t²

первая производная

v(t) =2+0,4t

Answer 2

To find the expression for v in terms of t (v = v(t)), we need to differentiate the given expression for X with respect to time (t) since v represents the velocity, which is the derivative of position (X) with respect to time.

Given: X = 2t + 0.2t²

To find v, take the derivative of X with respect to t:

v = dX/dt

v = d(2t + 0.2t²)/dt

Now, differentiate each term with respect to t:

v = d(2t)/dt + d(0.2t²)/dt

The derivative of 2t with respect to t is just 2 since the derivative of t with respect to itself is 1.

The derivative of 0.2t² with respect to t can be found using the power rule: d/dt (at^n) = nat^(n-1), where a and n are constants.

So, d(0.2t²)/dt = 0.2 * 2 * t^(2-1) = 0.4t

Now, substitute these values back into the expression for v:

v = 2 + 0.4t

So, the expression for v in terms of t is:

v = 2 + 0.4t