Question

Mатериальная точка движется прямолинейно по закону S(t)= 13t + 2t^2 - Найти ее скорость в момент времени 4 сек

Answer 1

$s(t)= 13t + 2t^2$
$v(t)=s'(t)=13+4t$
$v(4)=13+4*4=13+16=29$

$v(4)=29$

Answer 2

Calculating the Velocity of a Moving Object

To find the velocity of a material point moving in a straight line according to the law \( S(t) = 13t + 2t^2 \) at the moment of time \( t = 4 \) seconds, we can use the derivative of the position function \( S(t) \) with respect to time \( t \) to find the velocity at that specific moment.

Deriving the Velocity Function

The velocity of the material point at time \( t \) is given by the derivative of the position function \( S(t) \) with respect to time \( t \). The derivative of \( S(t) \) is denoted as \( S'(t) \) or \( v(t) \), where \( v(t) \) represents the velocity function.

The position function \( S(t) = 13t + 2t^2 \) can be differentiated to find the velocity function \( v(t) \).

The derivative of \( S(t) \) with respect to \( t \) is: \[ v(t) = \frac{dS}{dt} = \frac{d}{dt}(13t + 2t^2) \]

Calculating the Velocity at \( t = 4 \) Seconds

To find the velocity at the specific moment of time \( t = 4 \) seconds, we can evaluate the velocity function \( v(t) \) at \( t = 4 \).

Let's calculate the velocity at \( t = 4 \) seconds using the derived velocity function.

\[ v(t) = 13 + 4t \]

Substitute \( t = 4 \) into the velocity function: \[ v(4) = 13 + 4(4) = 13 + 16 = 29 \]

Answer

The velocity of the material point at \( t = 4 \) seconds is 29 units.

This calculation is based on the given position function \( S(t) = 13t + 2t^2 \) and its derivative to find the velocity function.