91Ó°ÊÓ

Kinetic friction is the resisting force between two objects sliding past each other. In our case, it's the force that acts between the car tire and the road. When the car skidded, kinetic friction was at play, opposing the motion of the car.

Kinetic friction is dependent on two main factors:

• Normal Force: The force perpendicular to the contact surface. For a car on a level road, this is simply its weight, which is the mass times gravity (\(mg\)).
• Coefficient of Kinetic Friction (\(\mu\)): A dimensionless number representing the frictional properties of the surfaces. For example, a \(\mu\) of 0.48 indicates moderate friction.

The force of kinetic friction (\(f\)) can be calculated using:\[f = \mu \times \text{normal force} = \mu mg\]Since frictional force causes deceleration, we use it to find the car's acceleration during the skid. This force becomes crucial in the equations of motion used to determine the car's initial speed when the brakes were applied.

The equations of motion are essential tools in physics for describing the movement of objects under the influence of forces. For our problem, since the car came to a halt after skidding, we use the equation:\[V_{0}^{2} = V_{f}^{2} + 2ad\]Here,

• \(V_{0}\): Initial velocity, which we need to determine.
• \(V_{f}\): Final velocity, 0 \(\mathrm{m/s}\) because the car stops.
• \(a\): Acceleration, which is negative because the car is slowing down. It is calculated using the friction force formula.
• \(d\): Distance over which the car skidded, given as 88 meters.

This equation allows us to calculate the initial velocity needed for the car to stop over a given distance with known friction, effectively tying together the concepts of friction, force, and motion.

Determining initial velocity (\(V_{0}\)) involves substituting known values into the equation of motion. We've identified our parameters: \(V_{f} = 0\), \(a = -4.704 \, \mathrm{m/s}^{2}\), and \(d = 88 \, \mathrm{m}\).

Substitute into:\[V_{0}^{2} = V_{f}^{2} + 2ad\]This becomes:\[V_{0}^{2} = 0^{2} + 2(-4.704)(-88)\]Simplifying yields:\[V_{0}^{2} = 826.6624\]Taking the square root of both sides gives:\[V_{0} \approx 28.75 \, \mathrm{m/s}\]This calculated initial velocity reflects how quickly the car was moving before the driver applied the brakes. Having a thorough understanding of these calculations is invaluable for problem-solving in physics, especially when evaluating forces and motion related to real-life scenarios.