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You are riding a bicycle. If you apply a forward force of 150 N, and you and the bicycle have a combined mass of 90 kg, what will be the forward acceleration of the bicycle? (Assume there is no friction.)

A. [tex]$0.60 \, \text{m/s}^2$[/tex]

B. [tex]$1.67 \, \text{m/s}^2$[/tex]

C. [tex][tex]$1.85 \, \text{m/s}^2$[/tex][/tex]

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


Sagot :

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]