Answer :
Sure, let's solve this problem step-by-step.
The question involves calculating the forward acceleration of a bicycle that is subject to a known force, given the combined mass of the rider and the bicycle.
We use Newton's second law of motion, which is given by:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
We need to solve for [tex]\( a \)[/tex] (acceleration), so we rearrange the formula:
[tex]\[ a = \frac{F}{m} \][/tex]
Given in the problem:
- The forward force [tex]\( F \)[/tex] = 172 N (Newtons)
- The combined mass [tex]\( m \)[/tex] = 51 kg (kilograms)
Now, we can plug these values into the equation:
[tex]\[ a = \frac{172\ \text{N}}{51\ \text{kg}} \][/tex]
When we divide 172 by 51, we get:
[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].
Therefore, the correct answer is:
A. [tex]\( 3.37\ m / s ^2 \)[/tex]
The question involves calculating the forward acceleration of a bicycle that is subject to a known force, given the combined mass of the rider and the bicycle.
We use Newton's second law of motion, which is given by:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration.
We need to solve for [tex]\( a \)[/tex] (acceleration), so we rearrange the formula:
[tex]\[ a = \frac{F}{m} \][/tex]
Given in the problem:
- The forward force [tex]\( F \)[/tex] = 172 N (Newtons)
- The combined mass [tex]\( m \)[/tex] = 51 kg (kilograms)
Now, we can plug these values into the equation:
[tex]\[ a = \frac{172\ \text{N}}{51\ \text{kg}} \][/tex]
When we divide 172 by 51, we get:
[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].
Therefore, the correct answer is:
A. [tex]\( 3.37\ m / s ^2 \)[/tex]
