Which will be moving faster after 3.0 s, a cyclist maintaining a constant velocity of 15 m/s straight ahead or a race car accelerating forward from a stoplight at 4.0 m/s^2″
The Correct Answer and Explanation is:
To determine which object will be moving faster after 3.0 seconds—a cyclist maintaining a constant velocity of 15 m/s or a race car accelerating from rest at 4.0 m/s²—we can use the equations of motion.
Cyclist’s Velocity
The cyclist is traveling at a constant velocity of 15 m/s. Thus, the speed after any time period remains the same:
[
v_{\text{cyclist}} = 15 \, \text{m/s}
]
Race Car’s Velocity
The race car starts from rest (initial velocity (u = 0)) and accelerates at a rate of (a = 4.0 \, \text{m/s}^2). We can calculate its velocity after 3.0 seconds using the formula for velocity under constant acceleration:
[
v = u + at
]
Substituting the known values:
[
v_{\text{car}} = 0 + (4.0 \, \text{m/s}^2)(3.0 \, \text{s}) = 12.0 \, \text{m/s}
]
Comparison
Now, we compare the velocities after 3.0 seconds:
- Cyclist’s velocity: (15 \, \text{m/s})
- Race car’s velocity: (12 \, \text{m/s})
From the calculations, the cyclist is moving faster at 15 m/s compared to the race car’s 12 m/s after 3.0 seconds.
Conclusion
Thus, after 3.0 seconds, the cyclist maintaining a constant velocity of 15 m/s will be moving faster than the race car, which is only able to reach 12 m/s after accelerating from rest. This scenario illustrates how constant speed can sometimes outperform acceleration over a short time period, especially when the acceleration is moderate, as in the case of the race car.