Question

A driver of an 8,000 kg car that is moving horizontally with a speed of 10 m/s applies brakes and locks the wheels to stop.

What would be the length of the skid marks, if the magnitude of the friction force is 80,000 N?

Answer and Full Detailed Explanation

Step 1: Understand the Given Data

• Mass (m) = 8000 kg
• Initial velocity (u) = 10 m/s
• Final velocity (v) = 0 m/s (car comes to rest)
• Friction force (f) = 80,000 N

Step 2: Apply Work-Energy Theorem

The work done by friction is equal to the change in kinetic energy:
f × s = ½ × m × u²

Step 3: Substitute the Values

80,000 × s = ½ × 8,000 × 10²

80,000 × s = 4,000 × 100 = 400,000

Step 4: Solve for s (Skid Length)

s = 400,000 / 80,000 = 5 m

Therefore, the length of the skid marks is 5 meters.