Question

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 if its trailer leaks sand at a constant rate through a hole in its bottom? (a) It decreases at a steady rate. (b) It increases at a steady rate. (c) It increases and then decreases. (d) It decreases and then increases. (e) It remains constant.

Short answer

The correct option is (b): It increases at a steady state.

Step-by-step solution

Write the given data from the question

The driving force on the truck is constant.

The flow of sand from the hole is constant.

Determine the formula to find the effect on the acceleration

The equation to calculate the force acting on the truck is as follows.

$\mathbf{F}\mathbf{=}\mathbf{ma}$

Here, m is the mass, and a is the acceleration.

 Step 3: Find the effect on the acceleration of sand leakage from the hole

Derive the equation for the acceleration from equation (1).

$$\begin{gathered} \mathrm{F}=\mathrm{ma} \\ \mathrm{a}=\frac{\mathrm{F}}{\mathrm{m}} \end{gathered}$$

Since the driving force on the truck is constant, the acceleration of the truck is inversely proportional to the mass of the truck.

$\mathrm{a}\propto \frac{1}{\mathrm{m}}$

From the above relation, the sand decreases from the hole, and the mass of the truck decreases, increasing the acceleration of the truck.

Hence, the acceleration of the truck increases at a steady state.