If a truck carrying a crate on its bed brakes hard enough that the crate slides to the right relative to the truck the distance d between the crate and the front of the trailer changes according to the relation
d = ukg + aT for td = ukg for t >ts
where ts is the time it takes the truck to stop, aT is the acceleration of the truck, g is the acceleration of gravity and uk is the kinectic friction coefficient between the truck and the crate. suppose that the truck and the crate are initially travelling to the right at v0 = 60 mph and the brakes are applied so that aT = -10ft/s^2 . Determine the minimum value of uk so that the crate does not hi the right end of the truck bed if the initial distance d is 12 feet.