Question

Тело движется по закону S(t) = t + 0,4t^2 - 6(m), где t - время движения в секундах. Найдите скорость тела через 10 секунд после начала движения.

Answer 1

Ответ:

8 м/с.

Пошаговое объяснение:

$s(t)=0,4t^{2} -6$

По физическому смыслу производной

$s'(t) =v(t)$

Найдем производную функции

$s'(t)=(0,4t^{2} -6)'=0,4\cdot2t=0,8t$

$v(t)=0,8t$

Надо определить скорость тела при t=10 c

$v(10)=0,8\cdot10=8$ (м/с)

Answer 2

Finding the Velocity of an Object

To find the velocity of an object at a specific time, we can differentiate the position function with respect to time. In this case, the position function is given by:

S(t) = t + 0.4t^2 - 6

To find the velocity, we need to differentiate this function with respect to time (t). The derivative of the position function will give us the velocity function.

Differentiating the Position Function

Let's differentiate the position function S(t) to find the velocity function V(t):

V(t) = d/dt (t + 0.4t^2 - 6)

Differentiating each term separately:

V(t) = d/dt (t) + d/dt (0.4t^2) - d/dt (6)

The derivative of t with respect to t is 1, the derivative of 0.4t^2 with respect to t is 0.8t, and the derivative of 6 with respect to t is 0 (since it is a constant).

V(t) = 1 + 0.8t - 0

Simplifying the expression:

V(t) = 1 + 0.8t

Finding the Velocity at t = 10 seconds

To find the velocity of the object at t = 10 seconds, we substitute t = 10 into the velocity function V(t):

V(10) = 1 + 0.8(10)

Calculating the expression:

V(10) = 1 + 8

V(10) = 9

Therefore, the velocity of the object at 10 seconds after the start of the motion is 9 units per second.

Please note that the units for velocity were not specified in the given question, so we have used generic units.