Answer:
[tex]250\; {\rm N}[/tex], assuming that the sand exerts a constant force.
Explanation:
If the sand exerts a constant force, acceleration (deceleration) would be constant. Let [tex]a[/tex] denote this acceleration.
It is given that:
Additionally, final velocity is [tex]v = 0\; {\rm m\cdot s^{-1}}[/tex] when the object is at rest.
Rearrange the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] to find acceleration [tex]a[/tex]:
[tex]\begin{aligned}a &= \frac{v^{2} - u^{2}}{2\, x} \\ &= \frac{{(0\; {\rm m\cdot s^{-1}})}^{2} - {(100\; {\rm m\cdot s^{-1}})}^{2}}{2\, (0.4\; {\rm m})} \\ &= (-12500)\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
Multiply acceleration by mass to find the net force:
[tex]\begin{aligned}(\text{net force}) &= m\, a \\ &= (0.02\; {\rm kg})\, (-12500\; {\rm m\cdot s^{-2}}) \\ &= (-250)\; {\rm {N}}\end{aligned}[/tex].
(Negative since velocity is decreasing.)
Assuming that all other forces are negligible. The force that the sand exerted would be equal to the net force, [tex](-250)\; {\rm N}[/tex] (negative since this force opposes the motion.)
