car that weighs 1200kg travels at 17 m/s and quickly stops. the car slides. coefficient of friction is 0.89. what is the distance the car slid?

Question

doing a physics question due tonight and im stuck... please help

Answer 1

We will solve this problem using the principle of conservation of energy.

The kinetic energy of the car changed (it was moving, then it stopped) by ΔE_k = M v₀² / 2

This change of energy is because of the work performed by the force of friction.

Work = Force times Distance

Force = μ M g

Distance = ( M v₀² / 2 ) / ( μ M g ) = ( v₀² ) / ( 2 μ g ) = (17 * 17) / (2 * 0.89 * 9.81) m = 17 m

Interestingly, the mass of the car does not matter here

Alternatively we can solve the problem using Newton's Second Law

F = M a

a = F / M = ( μ M g ) / M = - μ g (negative sign, because it is in the opposite direction from the car's velocity as the car is slowing down)

Then we can find distance using the equation

v² = v₀² + 2 a (x - x₀ ) , where v = 0, because the car stopped

Distance = x - x₀ = - v₀² / 2 a = v₀² / 2 μ g = (17 * 17) / (2 * 0.89 * 9.81) m = 17 m