Question

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.

Answer 1

The question is incomplete, here is a complete question.

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

$\Delta P=F\times \Delta t\\\\m\nu_f-m\nu_i=F\times \Delta t\\\\m(\nu_f-\nu_i)=\mu \times m\times g\times \Delta t\\\\(\nu_f-\nu_i)=\mu \times g\times \Delta t$

where,

m = mass

g = acceleration due to gravity = $9.8m/s^2$

$\mu$ = coefficient of kinetic friction = 0.25

$\nu_f$ = final velocity = 8.0 m/s

$\nu_i$ = initial velocity = 5.0 m/s

t = time

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

$(\nu_f-\nu_i)=\mu \times g\times \Delta t$

$(8.0-5.0)=0.25\times 9.8\times \Delta t$

$\Delta t=1.2s$

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