Question

M=10 кг S=3t^2+t+4 (м) t=4 секунд Eкинетич.= ?

Answer 1

E_k=mv²/2
v(t)=s'(t)=(3t²+t+4)'=6t+1
v(t)=6t+1
v(4)=6*4+1=25
E_k=10*25²/2=3225(кг*м²/с²)
E_k=3225 Дж

(E_k  кинетическая энергия.)

Answer 2

To find the kinetic energy (Eк) of an object with mass (M) and displacement (S), we need to use the equation:

Eк = (1/2) M v^2

Where: M = mass of the object v = velocity of the object

First, let's calculate the velocity (v) using the given displacement (S) and time (t).

Given: M = 10 kg S = 3t^2 + t + 4 (m) t = 4 seconds

To find the velocity (v), we need to differentiate the displacement equation (S) with respect to time (t):

v = dS/dt

Differentiating the equation S = 3t^2 + t + 4 with respect to t, we get:

v = d(3t^2 + t + 4)/dt = 6t + 1

Now, substitute the value of t = 4 seconds into the equation to find the velocity:

v = 6(4) + 1 = 24 + 1 = 25 m/s

Now that we have the velocity, we can calculate the kinetic energy (Eк) using the mass (M) and velocity (v) values:

Eк = (1/2) M v^2 = (1/2) * 10 kg * (25 m/s)^2 = 0.5 * 10 kg * 625 m^2/s^2 = 3125 Joules

Therefore, the kinetic energy of the object is 3125 Joules.