A20-kg box rests on the flat floor of a truck. the coefficients of friction between the box and floor are μs = 0.15 and μk = 0.10. the truck stops at a stop sign and then starts to move, with an acceleration of 2.0 m/s².
a) if the box is 5.0 m from the rear of the truck when it starts, how much time elapses before it falls off the rear of the truck? 3.13 s
b) how far does the truck travel in this time?

a) 3.16s

b) 10m

Explanation:

Let g = 10m/s2. Gravity and normal forces acting on the box:

N = G = mg= 20*10 = 200 N

The static friction acting on the box is

Kinetic friction acting on the box is:

When the truck accelerates from rest, this acceleration would generate an inertia force on the box

Since the box is definitely moving with respect to the truck with a net force of

So then the net acceleration of the box with respect to the truck is

a) the distance to the rear truck is 5m, then the time it takes for the box to accelerate and reach that point is

b) The distance travelled by the truck when it starts from rest: