Final answer:
The initial velocity of the car can be found by equating the work done by friction to the initial kinetic energy of the car. By using the work-energy principle and the given values, the initial velocity is calculated to be 20 m/s. Option A is correct.
Step-by-step explanation:
To calculate the initial velocity of the car, we can use the work-energy principle, which relates the work done by the frictional force to the kinetic energy of the car. Since the car skids to a stop, its final kinetic energy is 0, so the work done by friction is equal to the initial kinetic energy of the car. The work done by friction (Work = force × distance) is therefore:
Work = (frictional force) × (distance) = (7000 N) × (45 m) = 315,000 J.
The initial kinetic energy (KE) of the car, which is also 315,000 J since the car stops, is given by:
KE = 0.5 × (mass) × (initial velocity)2
We can rearrange this to solve for the initial velocity (v0):
v0 = √(2 × KE / mass) = √(2 × 315,000 J / 1575 kg) ≈ √(400) m/s ≈ 20 m/s.
Thus, the initial velocity of the car is 20 m/s (Option A).
To find the initial velocity of the car, we can use the equation:
Final velocity2 = Initial velocity2 + 2 * acceleration * distance
Since the car comes to a stop, the final velocity is 0 m/s. The acceleration can be calculated using Newton's second law:
Force = mass * acceleration
Substituting the given values into the equations, we can solve for the initial velocity:
0 = Initial velocity2 + 2 * (Force / mass) * distance
Initial velocity = √(-2 * (Force / mass) * distance)
Plugging in the values for the force, mass, and distance, we get:
Initial velocity = √(-2 * (7000 / 1575) * 45) ≈ 20 m/s
Therefore, the initial velocity of the car is approximately 20 m/s (Option A).