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

Answer :

To find the acceleration, we use Newton's second law, which states:

[tex]$$
F = m \cdot a
$$[/tex]

where
[tex]\( F \)[/tex] is the force applied,
[tex]\( m \)[/tex] is the mass, and
[tex]\( a \)[/tex] is the acceleration.

We are given:
- [tex]\( F = 172 \, \text{N} \)[/tex]
- [tex]\( m = 51 \, \text{kg} \)[/tex]

We can solve for [tex]\( a \)[/tex] by rearranging the equation:

[tex]$$
a = \frac{F}{m}
$$[/tex]

Substitute the given values:

[tex]$$
a = \frac{172}{51} \approx 3.37 \, \text{m/s}^2
$$[/tex]

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

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