If an object is moving at #7# #ms^-1# over a surface with a kinetic friction coefficient of #u_k=14 /g#, how far will the object continue to move?

Answer 1

Finding the frictional force and the acceleration due to it allows us to find the distance traveled, #1.75# #m#, before the object stops.

The force accelerating (decelerating) the mass will be the frictional force, which is the frictional coefficient times the normal force:

#F_"fric"=muF_N#

In this case the normal force is the weight force of the object:

#F_N=mg#

So

#F_"fric"=mumg=14/g*m*g#
#g# cancels out to leave a frictional force of #14m# where #m# is the mass. We don't know it, but be patient. ;-)

The acceleration (deceleration) of the object with this force acting on it is given by Newton's Second Law :

#a=F/m=(14m)/m=14# #ms^-2# (#m# cancels)

This should be given a minus sign, because it is an acceleration in the opposite direction to the object's velocity - a deceleration.

#a=-14# #ms^-2#
We know the initial velocity #u=7# #ms^-1# and the final velocity #v=0# #ms^-1# and the acceleration, and we are asked for the distance the object moves before stopping.
#v^2=u^2+2ad#

Rearranging:

#d=(v^2-u^2)/(2a)=(0^2-7^2)/(2*-14)=49/28 = 1.75 m#
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Answer 2

The object will continue to move for a distance determined by the equation: distance = (initial velocity^2) / (2 * friction coefficient * gravity). Plugging in the values, the distance can be calculated.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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