Question

материальная точка движется прямолинейно по закону x (t) = 1/3t^3-t^2+3t. тогда скорость точки в момент времени t=1 равна

Answer 1

v(t)=x'(t)=t^2-2t+3

v(1)=1-2+3=2

Answer 2

это производная  от x'(t)

x'(t)=   t^2-2t+3

x'(1)= 1-2+3=2

Answer 3

Calculating the Velocity of a Moving Point

To calculate the velocity of the point at time *t=1*, we can use the given position function *x(t) = 1/3t^3 - t^2 + 3t* and differentiate it with respect to time to find the velocity function.

Calculating Velocity

The velocity of the point at time *t* is given by the derivative of the position function *x(t)* with respect to time: *v(t) = x'(t) = (1/3t^3 - t^2 + 3t)'*

Using the power rule for differentiation, we get: *v(t) = 3*(1/3)t^2 - 2t + 3* *v(t) = t^2 - 2t + 3*

Now, to find the velocity at *t=1*, we substitute *t=1* into the velocity function: *v(1) = 1^2 - 2*1 + 3*

Calculating the Velocity at t=1

*v(1) = 1 - 2 + 3 = 2*

Therefore, the velocity of the point at time *t=1* is 2.