To determine the forward acceleration of the bicycle when a force is applied, we can use Newton's second law of motion. Newton's second law states that the force [tex]\( F \)[/tex] applied to an object is equal to the mass [tex]\( m \)[/tex] of the object multiplied by the acceleration [tex]\( a \)[/tex] of the object. This can be expressed with the formula:
[tex]\[ F = m \cdot a \][/tex]
Given the problem, we need to find the acceleration [tex]\( a \)[/tex]. We can rearrange the formula to solve for acceleration:
[tex]\[ a = \frac{F}{m} \][/tex]
The values provided are:
- Force [tex]\( F = 150 \, \text{N} \)[/tex]
- Mass [tex]\( m = 90 \, \text{kg} \)[/tex]
Substituting these values into the formula, we get:
[tex]\[ a = \frac{150 \, \text{N}}{90 \, \text{kg}} \][/tex]
[tex]\[ a = 1.6666666666666667 \, \text{m/s}^2 \][/tex]
Therefore, the forward acceleration of the bicycle is approximately [tex]\( 1.67 \, \text{m/s}^2 \)[/tex].
Hence, the correct answer is:
[tex]\[ B. \, 1.67 \, m/s^2 \][/tex]
