A sled slides along a horizontal surface for which the coefficient of kinetic friction is 0.25. Its velocity at point a is 8.0m/s and at point b is 5.0m/s.

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A sled slides along a horizontal surface for which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0m/s and at point B is 5.0m/s.

Use the impulse-momentum theorem to find how long the sled takes to travel from A to B.

Answer : The sled takes time to travel from A to B is, 1.2 seconds.

Explanation :

Impulse-momentum theorem:

Impulse = Change in momentum

[tex]\Delta P=F\times \Delta t\\\\m\nu_f-m\nu_i=F\times \Delta t\\\\m(\nu_f-\nu_i)=\mu \times m\times g\times \Delta t\\\\(\nu_f-\nu_i)=\mu \times g\times \Delta t[/tex]

where,

m = mass

g = acceleration due to gravity = [tex]9.8m/s^2[/tex]

[tex]\mu[/tex] = coefficient of kinetic friction = 0.25

[tex]\nu_f[/tex] = final velocity = 8.0 m/s

[tex]\nu_i[/tex] = initial velocity = 5.0 m/s

t = time

Now put all the given values in the above formula, we get:

[tex](\nu_f-\nu_i)=\mu \times g\times \Delta t[/tex]

[tex](8.0-5.0)=0.25\times 9.8\times \Delta t[/tex]

[tex]\Delta t=1.2s[/tex]

Therefore, the sled takes time to travel from A to B is, 1.2 seconds.

The sled is decelerating due to kinetic friction, and we can calculate this deceleration using the equations of motion and the given coefficient of kinetic friction. The normal force on the sled can also be found by dividing the frictional force by the coefficient of kinetic friction.

This problem pertains to the concept of kinetic friction and motion in Physics. We know that the sled's velocity decreases from 8.0m/s to 5.0m/s over some distance, which implies that it's decelerating due to kinetic friction. We can make use of the equation of motion v^2 = u^2 - 2*a*d where v is final velocity, u is initial velocity, a is deceleration (friction) and d is distance.

First, let's find the deceleration caused by the friction force using this equation. As we know that the frictional force can be expressed as F_kinetic = μk*m*g, where m is the mass of the sled (not given) and g is the acceleration due to gravity (9.8 m/s^2). From here, we can also find the normal force on the sled by knowing that the normal force is equal to kinetic friction divided by the coefficient of kinetic friction.

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