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A bicycle has a momentum of [tex]$36 \, \text{kg} \cdot \text{m/s}$[/tex] and a velocity of [tex]$4 \, \text{m/s}$[/tex]. What is the mass of the bicycle?

A. 9 kg
B. 32 kg
C. 40 kg
D. 144 kg

Answer :

To solve this problem, recall the formula that relates momentum, mass, and velocity. The momentum equation is given by

[tex]$$
p = m \cdot v,
$$[/tex]

where
- [tex]$p$[/tex] is the momentum,
- [tex]$m$[/tex] is the mass, and
- [tex]$v$[/tex] is the velocity.

We are given that the momentum is [tex]$36\,\text{kg}\cdot\text{m/s}$[/tex] and the velocity is [tex]$4\,\text{m/s}$[/tex]. To find the mass, we rearrange the equation to solve for [tex]$m$[/tex]:

[tex]$$
m = \frac{p}{v}.
$$[/tex]

Substituting the given values into the equation:

[tex]$$
m = \frac{36\,\text{kg}\cdot\text{m/s}}{4\,\text{m/s}}.
$$[/tex]

Performing the division:

[tex]$$
m = 9\,\text{kg}.
$$[/tex]

Thus, the mass of the bicycle is [tex]$\boxed{9\,\text{kg}}$[/tex].

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