Question

Тело массой 100 кг движется прямолинейно по закону s=2t^2+3t+1.Найти кинетическую энергию тела через 5 сек после начала движения.

Answer 1

V(t)=4*t+3
V(5)=4*5+3=23 м/с
Ek=m*V^2/2=0,1*23^2/2=26,5 Дж

Answer 2

Problem Analysis

We are given that a body with a mass of 100 kg is moving in a straight line according to the equation s = 2t^2 + 3t + 1, where s is the displacement in meters and t is the time in seconds. We need to find the kinetic energy of the body after 5 seconds.

Solution

To find the kinetic energy of the body, we need to know its velocity. The velocity can be obtained by taking the derivative of the displacement equation with respect to time.

Let's differentiate the equation s = 2t^2 + 3t + 1 with respect to t to find the velocity equation.

Differentiating the equation, we get:

v = ds/dt = d(2t^2 + 3t + 1)/dt

Taking the derivative of each term, we have:

v = 4t + 3

Now that we have the velocity equation, we can find the velocity of the body after 5 seconds by substituting t = 5 into the equation:

v = 4(5) + 3 = 20 + 3 = 23 m/s.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = (1/2)mv^2

where m is the mass of the object and v is its velocity.

Substituting the given values, we have:

KE = (1/2)(100 kg)(23 m/s)^2

Calculating this expression, we find:

KE = (1/2)(100 kg)(529 m^2/s^2) = 26,450 J

Therefore, the kinetic energy of the body after 5 seconds is 26,450 Joules.