Determine how much the tow rope with a rigidity of 40kN / m will stretch when towing a car weighing 1200 kg

Determine how much the tow rope with a rigidity of 40kN / m will stretch when towing a car weighing 1200 kg with an acceleration of 0.3 m / s squared. Disregard the friction force.

Let’s direct the X-axis in the direction of the vehicle. At the point of attachment of the cable to the car, two forces lying along one straight line and oppositely directed forces are applied: the elastic force of the cable Fel = kx, and the force, according to Newton’s second law, equal to F = Ma, where M is the mass of the car, a is the acceleration, k is the stiffness of the cable , x is its lengthening. According to Newton’s third law, these forces are equal: Fcont = F, or kx = Ma. Find x:
x = Ma / k = 0.009 m = 9mm.
Answer: 9mm.