You are called as an expert witness in a trial for a traffic...

You are called as an expert witness in a trial for a traffic violation. The facts are these: A driver slammed on his brakes and came to a stop with constant acceleration. Measurements of his tires and the skid marks on the pavement indicate that he locked his car's wheels, the car traveled 192 ft before stopping, and the coefficient of kinetic friction between the road and his tires was 0.750. He was charged with speeding in a 45-mi/h zone but pleads innocent. What is your conclusion: guilty or innocent? How fast was he going when he hit his brakes?

Key Concepts

Coefficient of Kinetic Friction

The coefficient of kinetic friction is a dimensionless scalar that quantifies the frictional force resisting the sliding motion between two contacting surfaces. It is crucial in determining the deceleration produced when an object, such as a vehicle, slides on a surface under kinetic friction.

Constant Acceleration Kinematics

Constant acceleration kinematics involves the use of equations that relate displacement, initial velocity, acceleration, and time. These equations allow for the analysis of motion when an object is uniformly decelerating or accelerating, and are fundamental in calculating parameters like stopping distance and speed from known values.

Braking Dynamics

Braking dynamics studies the processes and forces involved when a vehicle decelerates, particularly due to the friction between the tires and the road surface. This area of study integrates concepts from both friction and kinematics to assess vehicle safety, calculate braking distances, and understand the impact of deceleration forces during stoppages.

Unit Conversion in Physics

Unit conversion is the process of converting one set of measurement units to another to maintain consistency in physical calculations. In problems involving motion and friction, converting speeds and distances between units (for example, miles per hour to feet per second) is essential for accurate analysis and application of the relevant kinematic equations.

Transcript

00:02 Okay, this is question 586 traffic court.

00:03 We are called as an expert witness in a trial for a traffic violation.

00:07 A driver slammed on his brakes and came to a stop with constant acceleration.

00:11 And he locked his car wheels and then the car traveled 192 feet before stopping.

00:17 And then we know the coefficient of kinetic friction between the road and his tires.

00:22 So he was charged with speeding in a 45 -mile -for -hour zone but pleads innocent.

00:27 And we're trying to determine whether he's guilty or in.

00:30 Innocent.

00:31 So essentially what we want to figure out is what was his actual velocity before he slammed on the brakes and then decelerated at this constant rate due to the friction force.

00:41 So to do that, we're going to need to figure out what our actual acceleration, what his actual acceleration was first.

00:50 So to do that, we're going to use newton's second law.

00:53 So let's think about the sum of the forces in the x direction since the car is going to, let's just say it's moving.

01:00 In the x direction.

01:01 So the forces acting on the car, since he's already slammed on the brakes, are just going to be the friction force.

01:10 And the friction force is going to be negative, because it's going to be opposing the direction of the motion.

01:18 It's going to be slowing down the car, and that will be equal to the mass times the acceleration.

01:23 So we're going to get a negative number for the acceleration here, which indicates that it's decelerating.

01:29 So, the frictional force is going to be equal to the coefficient of kinetic friction times the normal force.

01:38 And the normal force here is just going to be mg because the car's weight is the only thing, the only vertical force that we have here...

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