Question

A truck loaded with sand accelerates along a highway. The driving force on the truck remains constant. What happens to the acceleration of the truck as its trailer leaks sand at a constant rate through a hole in its bottom?
(A) It increases at a steady rate.
(B) It remains constant.
(C) It decreases at a steady rate.
(D) It increases and then decreases.
(E) It decreases and then increases.

Answer 1

Answer:

As the trailer leaks sand at a constant rate through a hole in its bottom, its acceleration increases at a steady rate. (Option A)

Explanation:

F = ma

where;

F is the force applied on the truck

m is the mass of the truck

a is the acceleration of the truck

If the driving force on the truck remain constant, then;

m₁a₁ = m₂a₂

a₁ is the initial acceleration

a₂ is the final acceleration

m₁ is the initial mass of the truck and loaded sand,

m₂ is the final mass of the truck and loaded sand, which decreases as the sand leaks at a constant rate.

a₂ = (m₁a₁ )/(m₂)

since m₁ > m₂, a₂ > a₁

Therefore, as the trailer leaks sand at a constant rate through a hole in its bottom, its acceleration increases at a steady rate.