Question

The rear side of a truck is open and a box of mass $40kg$ is placed $5m$ away from the open end. The coefficient of friction between the box and the surface below it is $0.15$. The truck starts from rest with an acceleration of $2m{s}^{-2}$ on a straight road. At what distance from the starting point does the box fall off the truck?

• A. $20m$
• B. $30m$
• C. $40m$
• D. $50m$

Answer 1

The correct option is A $20m$

Given,
Mass of the box, $M=40kg$
Acceleration of the truck, $a=2m/s^{-2}$
Distance of the box from the rear end, $d=5m$
Coefficient of friction $\mu =0.15$
The truck moves in forward direction with the acceleration $a=2m/s^2$

Acceleration due to friction $a_f=\mu g=0.15\times 10=1.5m/s^2$

Let t be acceleration of the box relative to the truck toward the rear end is
$a_1=a-a_f=2-1.5=0.5m/s^2$

Apply kinematic equation

$s=ut+\frac{1}{2}a{t}^2$
$d=0\times t+\frac{1}{2}{a}_1{t}^2$ ($\because u=0$)
$5=\frac{1}{2}\times 0.5\times t^2,\Rightarrow t=\sqrt{\frac{2\times 5}{0.5}}=\sqrt{20}\sec$
Displacement of truck in time $t=\sqrt{20}\sec$
$S=ut+\frac{1}{2}a{t}^2$

$x=0\times t+\frac{1}{2}\times 2\times {\left(\sqrt{20}\right)}^2$

$x=20m$

Displacement of truck in time $t=\sqrt{20}\sec$ is $20m$.