Question

an unloaded when has an acceleration of 5 m/s². A fully loaded van weighs twice as much as the unloaded van. If the forward thrust on both vans is the same what is the acceleration of the fully loaded van?​

Answer 1

Correct Question

An unloaded van has an acceleration of 5 m/s². A fully loaded van weighs twice as much as the unloaded van. If the forward thrust on both vans is the same what is the acceleration of the fully loaded van?

Answer

• Acceleration of unloaded van = 5 m/s²
• Mass of Loaded van is twice the Mass of Unloaded van
• Acceleration of the fully loaded van = ?

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• So here we are given that the forward thrust is equal which means the force will be equal!!

$\sf :\implies F_1 = F_2$

$\sf \qquad\quad\small\dag \ \mathfrak{f = ma}$

$\sf :\implies m_1a_1 = m_2a_2$

$\sf :\implies \cancel{m_1} \times 5 = 2\times \cancel{m_2} \times a_2$

$\sf :\implies 5 = 2a_2$

$\sf :\implies \dfrac{5}{2} = a_2$

$\sf :\implies \pink{Acceleration = 2.5 \ m/s^2}$

$\displaystyle\therefore\:\underline{\textsf{Accn of the full loaded van is \textbf{ 2.5 m/s}}\bf{}^{2}}$

Answer 2

Explanation:

AnswEr :

$\LARGE \underbrace{\frak{\: \: \: \: \; \; \; \; \; \; \: \: \: \; \; \; \: Given \: \: \; \; \; \; \; \; \: \: \: \: \: \; \; \; \:}}$

$\boxed{\begin{minipage}{4cm} {\underline{\textsf{\textbf{For Unloaded Van :}}}} \\ \\ \bullet {\sf{Acceleration (a_1) = 5ms^{-2}}} \\ \\ \bullet \sf{Force = F_1} \\ \\ \bullet \sf{Mass = m_1} \end{minipage}}\boxed{\begin{minipage}{4cm} {\underline{\textsf{\textbf{For loaded Van :}}}} \\ \\ \bullet {\sf{Acceleration = a_2}} \\ \\ \bullet \sf{Force = F_2} \\ \\ \bullet \sf{Mass (m_2) = 2m_1} \end{minipage}}$

We're given F1 = F2

$\\ \\ : \implies \: \: \: \: \: \tt{F_1\ =\ F_2} \\ \\ \\ : \implies \: \: \: \: \: \tt{m_1 a_1\ =\ m_2\ a_2} \\ \\ \\ : \implies \: \: \: \: \: \tt{\cancel{m_1}\ \times\ 5\ =\ 2\cancel{m_1}\ \times\ a_2} \\ \\ \\ : \implies \: \: \: \: \: \tt{5\ =\ 2a_2} \\ \\ \\ : \implies \: \: \: \: \: \tt{a_2\ =\ \dfrac{5}{2}} \\ \\ \\ \large : \implies \: \: \: \: \: \underline{\boxed{\frak{a_2\ =\ 2.5\ ms^{-2}}}}$