The question deals with the kinematics in physics. We will use the equation of motion v² = u² + 2as to solve the problem, where:
- v is the final velocity of the car
- u is the initial velocity of the car (which we're trying to find)
- a is the acceleration (In our case, it's deceleration)
- s is the distance the car travels
Given that the car eventually comes to a stop, the final velocity v is 0. The acceleration a is negative in this case because the car is decelerating, and it's given as -4.50 m/s². The distance s the car travels is the length of the skid marks, given as s=71 m.
So, we can substitute these values into the equation:
0 = u² + 2*(-4.50)*71.
By moving the right side of the equation to the left, we get:
u² = 2*4.50*71.
Now, we need to solve for u, which is the speed of the car before it started braking or initial speed. Taking square root on both sides gives us:
u = √(2*4.50*71).
By evaluating the above expression, we get the speed of the car before it started braking as approximately 25.28 m/s.
Hence, the initial speed of the car before braking was approximately 25.28 m/s.