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You are riding a bicycle. If you apply a forward force of 172 N, and you and the bicycle have a combined mass of 51 kg, what will be the forward acceleration of the bicycle? (Assume there is no friction.)

A. [tex]0.30 \, \text{m/s}^2[/tex]
B. [tex]3.37 \, \text{m/s}^2[/tex]
C. [tex]1.67 \, \text{m/s}^2[/tex]
D. [tex]1.85 \, \text{m/s}^2[/tex]

Answer :

We are given a forward force of
[tex]$$F = 172 \text{ N}$$[/tex]
and a combined mass of
[tex]$$m = 51 \text{ kg}.$$[/tex]

According to Newton's second law, the acceleration [tex]$a$[/tex] can be determined by the formula:
[tex]$$a = \frac{F}{m}.$$[/tex]

Substituting the given values, we have:
[tex]$$a = \frac{172 \text{ N}}{51 \text{ kg}} \approx 3.37 \text{ m/s}^2.$$[/tex]

Thus, the forward acceleration of the bicycle is approximately
[tex]$$3.37 \text{ m/s}^2,$$[/tex]
which corresponds to option B.

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