Police examine the scene of an accident involving two cars, which is parked. The skid marks of the moving car, which nearly came to a stop before the collision, is 80 meters long. The coefficient of kinetic friction between rubber and the pavement is about .80. Estimate the initial speed of the car
35 m/s or 130 km/hr
To estimate the initial speed of the car, we can use the concept of work and energy.
First, let's gather the relevant information:
1. Skid marks length (d): 80 meters
2. Coefficient of kinetic friction (μ): 0.80
Now, let's proceed to the solution:
1. Identify the initial energy of the car:
- The only form of energy acting on the car is kinetic energy (since it is almost at a stop before the collision).
- The formula for kinetic energy is KE = 0.5 * m * v^2, where m is the mass of the car and v is its velocity.
- We can rewrite the kinetic energy formula as KE = (1/2) * m * v_initial^2, where v_initial is the initial velocity of the car.
2. Identify the work done by friction:
- The work done by friction can be calculated using the formula W = μ * m * g * d, where μ is the coefficient of kinetic friction, m is the mass of the car, g is the acceleration due to gravity (9.8 m/s^2), and d is the distance covered by the skid marks.
- We can rewrite the friction work formula as W = μ * m * g * 80.
3. Equate the work done by friction to the change in kinetic energy:
- Since we assume that there are no external forces acting on the car, the work done by friction is equal to the change in kinetic energy.
- Thus, we can equate W (friction work) to KE (change in kinetic energy) and solve for v_initial:
μ * m * g * 80 = (1/2) * m * v_initial^2.
- Note that the mass (m) cancels out.
4. Solve for v_initial:
- Rearrange the equation: v_initial^2 = 2 * μ * g * 80.
- Take the square root of both sides of the equation to get the value of v_initial: v_initial = √(2 * μ * g * 80).
5. Calculate v_initial:
- Substitute the values: v_initial = √(2 * 0.80 * 9.8 * 80).
- Evaluate the expression to find the initial velocity: v_initial ≈ 35.93 meters per second (m/s).
Therefore, the estimated initial speed of the car is approximately 35.93 m/s.