High School

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

Answer :

We can solve the problem using Newton's second law, which states that

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

where:
- [tex]$F$[/tex] is the force applied,
- [tex]$m$[/tex] is the mass,
- [tex]$a$[/tex] is the acceleration.

We are given that:
- [tex]$F = 172$[/tex] Newtons,
- [tex]$m = 51$[/tex] kilograms.

To find the acceleration [tex]$a$[/tex], we rearrange the formula:

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

Substitute the given values into the equation:

[tex]$$
a = \frac{172}{51}.
$$[/tex]

Performing the division:

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

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

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