To determine the forward acceleration of the bicycle when a force is applied, we use Newton's second law of motion. Newton's second law states that the acceleration [tex]\( a \)[/tex] of an object is directly proportional to the net force [tex]\( F \)[/tex] acting on it and inversely proportional to its mass [tex]\( m \)[/tex]. This relationship can be expressed with the formula:
[tex]\[ a = \frac{F}{m} \][/tex]
Given:
- The force applied [tex]\( F \)[/tex] is 125 Newtons (N)
- The combined mass of you and the bicycle [tex]\( m \)[/tex] is 82 kilograms (kg)
We need to find the acceleration [tex]\( a \)[/tex]. Plugging the given values into the formula:
[tex]\[ a = \frac{125 \, \text{N}}{82 \, \text{kg}} \][/tex]
Upon performing the division:
[tex]\[ a = \frac{125}{82} \approx 1.524390243902439 \][/tex]
Rounding the value to two decimal places, we get:
[tex]\[ a = 1.52 \, \text{m/s}^2 \][/tex]
So, the forward acceleration of the bicycle is approximately [tex]\( 1.52 \, \text{m/s}^2 \)[/tex].
From the given options, the correct answer is:
[tex]\[ \boxed{1.52 \, \text{m/s}^2} \][/tex]
