A runner is said to accelerate at 0.40 m/s^2 from rest for 100 s. What final speed does this give, and why is the result rejected?
A4.0 m/s, rejected because the acceleration is too small
B40 m/s, rejected because the time is an unreasonable premise
C40 m/s, rejected because the kinematic equation does not apply
D250 m/s, rejected because the acceleration is unreasonable
Answer & Solution
Correct answer: B. 40 m/s, rejected because the time is an unreasonable premise
1. The final velocity equals the initial velocity plus the acceleration times the time.
2. Substitute the values: 0 + (0.40 m/s^2)(100 s) = 40 m/s.
3. A speed of 40 m/s is about four times greater than a person can run, so it is too large.
4. An acceleration of 0.40 m/s^2 means the velocity rises by only 0.4 m/s each second, which is reasonable.
5. The suspect premise is therefore the time, since nobody can accelerate steadily for almost two minutes.
6. The physics was applied correctly, so blaming the equation misses the point.
_Source: OpenStax College Physics (CC BY 4.0), Ch 2 "Kinematics", section 2.6 Problem-Solving Basics for One-Dimensional Kinematics_
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