Answer
(a) $0.163s$
(b) $0.102m$
Work Step by Step
We can find the required time as follows:
$\Sigma F_x=-\mu_k mg=ma$
This simplifies to:
$a=-\mu_kg$
We also know that
$t=\frac{v_f-v_i}{a}$
$\implies t=\frac{v_f-v_i}{-\mu_kg}$
$\implies t=\frac{0-v_i}{-\mu_kg}$
We plug in the known values to obtain:
$t=\frac{1.25}{(0.780)(9.81)}$
$t=0.163s$
(b) The required distance can be determined as
$x=\frac{1}{2}(v_f+v_i)t$
We plug in the known values to obtain:
$x=\frac{1}{2}(0+1.25)(0.163)$
$x=0.102m$
