physics dynamic

Question

A large sport vehicle has a mass of 1850 kg and is traveling at 15m/s. The driver slams on the brakes, causing the vehicle to skid. How car would the SUV travel before it stops on asphalt? Static is 0.85 and kinetic is 0.67

Answer 1

This is a kinematics problem. Use the relation

v₂² - v₁² = 2ad

v₁ = initial speed = 15 m/s

v₂ = final speed = 0 (full stop)

d = distance required for speed to drop from v₁ to v₂

a = acceleration (which in this situation, is negative)

a = F/m = -μ_kmg / m = -μ_kg

μ_k = coefficient of kinetic friction = 0.67

Put it all together and get

v₁² = 2(μ_kg)d ⇒

d = v₁² / (2μ_kg)

Now plug in the given values of v₁, μ_k, and g, and get d in meters.