Answer :
Final answer:
The problem is solved by equating the initial kinetic energy of the cars (which is converted into work done by friction) to the work done against friction. Using this and the principle of conservation of momentum we can find the common initial velocity. However, without further data, finding the initial velocity of each car independently is not possible.
Explanation:
Given that both cars skid together to a halt (meaning they move as one mass), we can use the principle of conservation of momentum and the work-energy theorem to solve this problem.
It is given that the two cars together skidded for a distance of 54 meters on the road before stopping, with a coefficient of kinetic friction of 0.7. When friction stops them, all their initial kinetic energy is transformed into the work done by friction against the car’s movement. This can be represented as:
Work done by friction = 0.5*(mass of both cars)*v² = Friction force*distance = (mass of both cars * g * μ)*distance
Where: mass of both cars = 1200kg+1800kg = 3000kg, force of gravity(g) = 9.8ms²,μ is the coefficient of kinetic friction = 0.7, and distance = 54m.
Solving the equation for v (initial velocity of the combined mass of cars) gives us a common Velocity. Once we get the common speed,we use the principles of conservation of momentum, to find the initial velocities of both cars. Since the two cars get locked together,Either both cars were moving in the same direction or one was stationary. We don't have enough information to decide which case this is. This leads to multiple solutions for the initial speeds of the cars which is beyond the scope of high school physics.
Learn more about Physics: Work, Energy and Momentum here:
https://brainly.com/question/33525166
#SPJ11
