Answer
The minimum braking distance increases by a factor of 2.25.
Work Step by Step
The minimum braking distance is the distance required for the work done by the force of friction to equal the kinetic energy of the car.
$Work = KE$
$F_f ~d_1 = \frac{1}{2}mv^2$
$d_1 = \frac{mv^2}{2F_f}$
Let the velocity of the car be 1.5v.
$d_2 = \frac{m(1.5v)^2}{2F_f}$
$d_2 = 2.25\times\frac{mv^2}{2F_f}$
$d_2 = 2.25\times d_1$
The minimum braking distance increases by a factor of 2.25.
