The equation of motion of a car with a mass of 2 tons has the form: x = 10 + 5 * t²

The equation of motion of a car with a mass of 2 tons has the form: x = 10 + 5 * t² which is equal to the resultant of all forces acting on the body

Given:

m = 2 tons = 2000 kilograms – vehicle weight;

x (t) = 10 + 5 * t ^ 2 – the equation of motion of the car.

It is required to determine F (Newton) – the resultant of all forces acting on the car.

Let us find the equation of the dependence of the speed on time by fulfilling the derivative of the first degree of the equation of motion of the car:

v (t) = x (t) ’= (10 + 5 * t ^ 2)’ = 10 * t.

Let’s find the acceleration of the body:

a = v (t) ’= (10 * t)’ = 10 m / s2.

Then, according to Newton’s second law, the resultant of all forces will be equal to:

F = m * a = 2000 * 10 = 20,000 Newton = 20 kN.

Answer: the resultant of all forces acting on the car is 20 kN.