Question

Тело движется по прямой так, что расстояние S от начальной точки изменяется по закону S(t)= 0,5t^2+3t+4(м) где t - время движения в секундах. Найдите скорость тела через 2с после начала движения.

Answer 1

Т.к скорость это производная от пути, то:
v(t)=S(t)'=0,5*2t+3=t+3
v(2)=2+3=5
Ответ: 5 м/с

Answer 2

Problem Analysis

We are given the equation for the distance traveled by an object on a straight line, which is given by the equation S(t) = 0.5t^2 + 3t + 4, where t is the time in seconds. We need to find the velocity of the object after 2 seconds.

Solution

To find the velocity of the object, we need to find the derivative of the distance equation with respect to time. The derivative of S(t) will give us the velocity function.

Let's find the derivative of S(t):

S'(t) = (0.5t^2 + 3t + 4)'

Using the power rule of differentiation, we can differentiate each term separately:

S'(t) = (0.5t^2)' + (3t)' + (4)'

The derivative of t^n is nt^(n-1), and the derivative of a constant is 0. Applying these rules, we get:

S'(t) = 0.5 * 2t^(2-1) + 3 * 1t^(1-1) + 0

S'(t) = t + 3

Now, we can substitute t = 2 into the velocity function to find the velocity after 2 seconds:

v(2) = 2 + 3

v(2) = 5 m/s

Therefore, the velocity of the object after 2 seconds is 5 m/s.

Answer

The velocity of the object after 2 seconds is 5 m/s.