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

Sure, let's solve this problem step-by-step using Newton's second law of motion.

Newton's second law states that:

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

where:
- [tex]\( F \)[/tex] is the force applied (in Newtons, N)
- [tex]\( m \)[/tex] is the mass of the object (in kilograms, kg)
- [tex]\( a \)[/tex] is the acceleration (in meters per second squared, [tex]\(\text{m/s}^2\)[/tex])

We are given:
- [tex]\( F = 172 \)[/tex] N (forward force)
- [tex]\( m = 51 \)[/tex] kg (combined mass of you and the bicycle)

We need to find the acceleration [tex]\( a \)[/tex]. Let's rearrange the formula to solve for [tex]\( a \)[/tex]:

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

Now, plug in the given values:

[tex]\[
a = \frac{172 \, \text{N}}{51 \, \text{kg}}
\][/tex]

[tex]\[
a = 3.372549019607843 \, \text{m/s}^2
\][/tex]

So, the forward acceleration of the bicycle is approximately:

[tex]\[
a \approx 3.37 \, \text{m/s}^2
\][/tex]

Therefore, the correct answer is:

A. [tex]\(3.37 \, \text{m/s}^2\)[/tex]