On its own, a certain tow-truck has a maximum acceleration of 3.0 m/s2. what would be the maximum acceleration when this truck w

Question

user100

1 month ago

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On its own, a certain tow-truck has a maximum acceleration of 3.0 m/s2. what would be the maximum acceleration when this truck w

as towing a bus of twice its own mass?

Physics

2 answers:

serg [3.5K] · Answer 1 · 2026-02-21T19:11:06+03:00

The highest acceleration will be 1.0 m/s² when the truck is towing a bus that weighs twice as much as it does.

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Further explanation

According to Newton's second law of motion, the net force acting on an object is proportional to both its mass and its acceleration.

$\boxed {F = ma }$

F = Force (in Newtons)

m = Mass of Object (in kg)

a = Acceleration (in m/s²)

Now let's solve the problem!

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Given:

initial acceleration = a₁ = 3.0 m/s²

mass of tow-truck = m₁ = m

mass of bus = m₂ = 2m

Question:

final acceleration = a₂ =?

Solution:

$\texttt{Initial Force of Tow-Truck = Final Force of Tow-Truck }$

$F_1 = F_2$

$m_1 a_1 = m_2 a_2$

$m (3.0) = (m + 2m) a_2$

$3m = 3m (a_2)$

$a_2 = 3m \div 3m$

$\boxed{a_2 = 1.0 ~ \mathtt{ m/s^2}}$

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Conclusion:

The maximum acceleration would be 1.0 m/s²

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Learn more

Effects of Gravity:
Impact of Earth’s Gravity on Objects:
Acceleration Due to Gravity:
Newton's Law of Motion:
Newton's Law Examples:

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

inna [3.1K] · Answer 2 · 2026-02-21T19:13:21+03:00

Let us denote $a_1=3 m/s^2$ as the highest acceleration of the truck by itself. The force generated by the engine to propel the truck in this scenario is
$F= ma_1$
where m is the mass of the truck alone.

Upon attaching a bus that has double the mass of the truck, the total mass of the entire system (truck+bus) becomes (m+2m)=3m. In this situation, the force generated by the engine is
$F=3m a_2$
where a2 represents the new acceleration.
Since the engine remains unchanged, the force generated stays the same, allowing us to set the force equations equal to each other:
$m a_1 = 3 m a_2$
and solving for a2 gives us:
$a_2 = \frac{m a_1}{3 m}= \frac{a_1}{3}= \frac{3 m/s^2}{3}=1 m/s^2$