9. An accident reconstruction expert is called out to a crash scene. A car of ma

Question

9. An accident reconstruction expert is called out to a crash scene. A car of mass m and speed v had crashed into the rear of an identical parked car whose parking brake was set. The skid marks indicate that the joined cars traveled a distance x before coming to rest. The coefficient of friction between the tires and the road is 4 (a) Derive an equation for the initial speed of the incoming car. (b) Calculate the initial speed of the incoming car ifm = 1400 kg, = 0.65, and x-12 m. PHOTOGATE Diagram for roblems CARTA 40 through 6-42 AIR TRACK

Explanation / Answer

v = Initial vspeed of car 1

Mass of car 1 = Mass of car 2 = m

Initial momentum = final momentum

let final velocuty of joined cars = y

mv + 0 = (m+m)y

y = v/2

Distance travved before rest = x

acceleretion = deceleretion due to friction = usg (us = coefficient of friction)

v^2 - u^2 = 2as (Third equation of motion)

0 - (v/2)^2 = -2usgx

v^2/4 = 2usgx

v = sqrt(8usgx)

part b)

v = sqrt(8*0.65*9.8*12) = 24.73 m/s

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