An officer is investigating an accident. A car has struck a pedestrian at a school crosswalk.There are no witnesses to the accident. The officer measures the coefficient of friction at the accident site to be 0.55, and he measures skid marks that are 52m long. What is the minimum initial speed of the vehicle?

a = u*g = 0.55 * (-9.8) = -5.39 m/s^2.

V^2 = Vo^2 + 2a*d.
Vo^2 = V^2 - 2a*d. = 0 - 2(-5.39)*52 =
561.
Vo = 23.7 m/s.

To determine the minimum initial speed of the vehicle, we can use the concept of conservation of energy.

Here's how you can approach the problem:

1. Start by defining the given information:
- Coefficient of friction (µ) = 0.55
- Length of skid marks (s) = 52m

2. Understand the concept of work and energy:
- When a vehicle skids to a stop, the work done by the friction force is equal to the change in kinetic energy of the vehicle.
- The work done by friction is given by: W = µmgd, where m is the mass of the vehicle, g is the acceleration due to gravity (approximately 9.8 m/s²), and d is the stopping distance.

3. Calculate the stopping distance (d):
- The stopping distance (d) is given by d = s + µs, where s is the length of the skid marks.
- Substitute the given value for s into the equation: d = 52m + (0.55 * 52m).

4. Calculate the work done by friction (W):
- Substitute the values for µ (0.55), m (mass of the vehicle), g (9.8 m/s²), and d (stopping distance) into the equation W = µmgd.

5. Calculate the initial kinetic energy (KE) of the vehicle:
- The initial kinetic energy of the vehicle is equal to the work done by friction: KE = W.

6. Use the formula for kinetic energy (KE):
- The formula for kinetic energy is KE = 0.5mv², where m is the mass of the vehicle and v is the initial velocity of the vehicle.

7. Rearrange the equation:
- Rearrange the equation KE = 0.5mv² to isolate the initial velocity (v): v = sqrt((2KE)/m).

8. Substitute the value of KE from step 5 into the equation to get the minimum initial velocity.

Following these steps will help you determine the minimum initial speed of the vehicle involved in the accident.