Under the influence of its drive force, a snowmobile is moving at a constant vel

Question

Under the influence of its drive force, a snowmobile is moving at a constant velocity along a horizontal patch of snow. When the drive force is shut off, the snowmobile coasts is to a halt. The snowmobile and its rider have a mass of 130 kg. Under the influence of a drive force of 245 N, it is moving at a constant velocity whose magnitude is 4.67 m/s. The drive force is then shut off. Find (a) the distance in which the snowmobile coasts to a halt and (b) the time required to do so. (a) s = 1.24 m (b) t = 2.48 s

Explanation / Answer

(a) Since the snowmobile is moving with constant velocity, the net force acting on it must be zero.

Apart from the drive force, we have horizontal force of kinetic friction acting between the runners of the snowmobile and the snow.

Frictional force = - 245N (Minus to indicate this is opposite to the drive force)

When the drive force is shut off,

Dcceleration due to friction = force / mass = - 245/130 = -1.88 m/s2

Initial velocity (u) = 4.67m/s.
Acceleration (a) = -1.88 m/s^2
Final velocity = 0 m/s

Let s be the distance in which the snowmobile coasts to a halt

v2 - u2 = 2as

=> s =- u2 / 2a = - (4.67)^2 / [2*(-1.88)]

=> s = 5.8 m

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(b) Let t be the time required for the snowmobile to come to a halt

v = u + at

=> t = v-u /a = 0 - 4.67 / -1.88

=> t = 2.48 s

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