To find the acceleration of the bike and bike rider when the brakes apply a force of 100 N, we can use Newton's second law of motion, which states:
\[ F = m \cdot a \]
Where:
- \( F \) is the force applied (in newtons),
- \( m \) is the mass (in kilograms),
- \( a \) is the acceleration (in meters per second squared).
In this case, the total mass \( m \) of the bike and rider is 50 kg, and the braking force \( F \) is 100 N. Since the brakes are applying a force to stop the bike, we can consider this force as negative (i.e., it is acting in the opposite direction of the motion). Therefore, we can write the equation as:
\[ -100 = 50 \cdot a \]
Now, we solve for \( a \):
\[ a = \frac{-100}{50} = -2 , \text{m/s}^2 \]
The negative sign indicates that the acceleration is in the direction opposite to the motion, which is expected when the brakes are applied. Thus, the acceleration of the bike and rider is:
\[ a = -2 , \text{m/s}^2 \]
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