Question

Зависимость пройденного телом пути от времени имеет вид s = 2t - 3t2 +4t3 . Найти зависимость скорости от времени и силу, действующую на тело в конце второй секунды, Масса тела 1 кг.

Answer 1

S(t)=2t-3t^2+4t^3

 

v(t)=производной от S(t)=2-6t+12t^2

a(t)=второй производной от S(t)=-6+24t

 

при t=2 скорость v(2)=2-6*2+12*2^2=2-12+48=38

             путь S(t)=-6+24*2=-6+48=42

Answer 2

Equation for the Distance Traveled

The equation for the distance traveled by an object as a function of time is given as:

s = 2t - 3t^2 + 4t^3

where s represents the distance traveled and t represents time.

Finding the Velocity as a Function of Time

To find the velocity as a function of time, we need to differentiate the equation for distance with respect to time. The derivative of the distance equation will give us the velocity equation.

Differentiating the equation s = 2t - 3t^2 + 4t^3 with respect to time (t), we get:

v = ds/dt = 2 - 6t + 12t^2

where v represents the velocity of the object.

Finding the Force Acting on the Object at the End of the Second Second

To find the force acting on the object at the end of the second second, we need to differentiate the velocity equation with respect to time. The derivative of the velocity equation will give us the acceleration equation.

Differentiating the equation v = 2 - 6t + 12t^2 with respect to time (t), we get:

a = dv/dt = -6 + 24t

where a represents the acceleration of the object.

Since force (F) is equal to mass (m) multiplied by acceleration (a), we can calculate the force acting on the object at the end of the second second.

Given that the mass of the object is 1 kg, the force (F) can be calculated as:

F = m * a = 1 kg * (-6 + 24t)

Substituting t = 2 into the equation, we can find the force acting on the object at the end of the second second:

F = 1 kg * (-6 + 24 * 2)

Simplifying the equation, we get:

F = 1 kg * (-6 + 48) = 1 kg * 42 = 42 N

Therefore, the force acting on the object at the end of the second second is 42 Newtons (N).