Question

at the beginning of its route, a garbage truck accelerates at 10 m/s² as it is driven down the road. by the end of the route, the trucks mass has quadrupled. if the trucks force remains constant, what is the trucks acceleration at the end of the route? 20 m/s² 10 m/s² 2.5 m/s² 5 m/s²

Explanation:

Step1: Recall Newton's second - law

$F = ma$ (where $F$ is force, $m$ is mass, and $a$ is acceleration). Let the initial mass be $m_1$ and initial acceleration be $a_1 = 10\ m/s^2$, so the initial force $F_1=m_1a_1$.

Step2: Determine the final - state variables

The final mass $m_2 = 4m_1$ and the force remains constant, i.e., $F_1=F_2$. Since $F_2=m_2a_2$ and $F_1 = F_2$, we have $m_1a_1=m_2a_2$.

Step3: Substitute $m_2 = 4m_1$ into the equation

$m_1\times10 = 4m_1\times a_2$.

Step4: Solve for $a_2$

Dividing both sides of the equation $m_1\times10 = 4m_1\times a_2$ by $4m_1$ (assuming $m_1
eq0$), we get $a_2=\frac{10}{4}=2.5\ m/s^2$.

Answer:

$2.5\ m/s^2$