Under the influence of its drive force, a snowmobile is movingat a constant velo

Question

Under the influence of its drive force, a snowmobile is movingat a constant velocity along a horizontal patch of snow. When thedrive force is shut off, the snowmobile coasts to a halt. Thesnowmobile and its rider have a mass of 125 kg. Underthe influence of a drive force of 205 N, it is movingat a constant velocity whose magnitude is 5.47 m/s.The drive force is then shut off. Find (a) thedistance in which the snowmobile coasts to a halt and(b) the time required to do so.

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Explanation / Answer

(a)     we use the work energy theorem equation givenby     W = (1 / 2) m vf2 - (1 /2) m vo2    the work W isthe work done by the net force acting on the snowmobile        during the coasting phase, the net force actingon the snowmobile is the kinetic frictional force(magnitude = fk)     so the work W can be written as    W = (fk cos ) s     substituting in the work energy theorem we getthat    (fk cos ) s = (1 / 2) m vf2 - (1 / 2) mvo2     s = m (vf2 -vo2) / 2 fkcos   (b)     using the equation of motion we get that     s = (1 / 2) (vo + vf)t     t = 2 s / (vo + vf)       = ......... s

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