A vehicle is moving at a speed of $12.3\,\text{m/s}$ on a decline when the brakes of all four wheels are fully applied, causing them to lock. The slope of the decline forms an angle of $18.0^\circ$ with the horizontal plane. The coefficient of kinetic friction between the tires and the road surface is $0.650$.

Question

A vehicle is moving at a speed of $12.3\,\text{m/s}$ on a decline when the brakes of all four wheels are fully applied, causing them to lock. The slope of the decline forms an angle of $18.0^\circ$ with the horizontal plane. The coefficient of kinetic friction between the tires and the road surface is $0.650$.(a) Determine the distance $D$ the vehicle slides down the incline before it halts.
, (b) If the angle of the incline is increased by a factor of $1.5$, how much further would the vehicle slide? Give your answer in terms of $D$.
, (c) Now suppose the vehicle were to lock its brakes while traveling up the same incline with the same initial velocity. Would the vehicle travel a larger, shorter, or equal distance than in part (a)? Justify your answer.
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Jason · Accepted Answer

$d = 8.32 \,\text{meters}$
$d&#8217; = .89d$

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