The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in figure. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 `ms^(2)` . At what distance from the starting point does the box fall off the truck ? (Ignore the size of the box)

Explanation

Mass of block m= 40 kg
Acceleration of truck = `2ms^(-2)`
Froce acting on block due to acceleration motion of truck
`F = ma`
`=40 xx 2`
`=80 N`
Due to reaction on block it will try to move but because of friction force ti will not move
`f= muR`
`=0.15 xx 40 xx 9.8`
Net force
F=f-f
`=80 - 58.8`
`=21.2 N`
Backward acceleration in block
from the third equation motion
`5= 0 xx t + (1)/(2) xx 0.53 xx t^(2)`
Distance covered by truck in given time
`s= ut + (1)/(2) at^(2)`
` = 0 xx t+ (1)/( 2) xx 2 xx (4.34)^(2)`
`:. s = 18.87 m`