Under the influence of its drive force, a snowmobile is...

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 to a halt. The snowmobile and its rider have a mass of 136 kg. Under the influence of a drive force of $205 \mathrm{N}$, it is moving at a constant velocity whose magnitude is $5.50 \mathrm{m} / \mathrm{s}$. 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.

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Key Concepts

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the product of its mass and acceleration. This key concept is used to determine the deceleration (or negative acceleration) when the driving force is removed, making it possible to calculate the stopping time and distance of a moving object.

Equilibrium of Forces

When an object moves at constant velocity, the net force acting on it is zero, meaning that all forces are balanced. In this context, the driving force is exactly counteracted by friction, establishing an equilibrium state. Recognizing this balance allows us to determine the magnitude of the frictional force that will subsequently decelerate the object once the driving force is removed.

Uniformly Accelerated Motion

Uniformly accelerated motion, governed by kinematic equations, describes motion with constant acceleration. This concept provides the necessary formulas to calculate the stopping distance and the time taken to come to a halt when the object decelerates uniformly. The relationships between initial velocity, acceleration, time, and displacement are central to solving problems of coasting to rest.

Transcript

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