An object has maximum acceleration of 100 m s-2, amplitude 0.5 m and angular frequency 20 rad s-1. What is its maximum velocity?
Understand the Problem
The question is asking for the maximum velocity of an object given its maximum acceleration, amplitude, and angular frequency. To solve this, we can use the relationship between maximum acceleration, maximum velocity, amplitude, and angular frequency in harmonic motion.
Answer
The maximum velocity is $10 \, \text{m/s}$.
Answer for screen readers
The maximum velocity is $10 , \text{m/s}$.
Steps to Solve
- Identify the formula for maximum velocity
In harmonic motion, the maximum velocity ($V_{max}$) can be found using the formula: $$ V_{max} = A \omega $$ where $A$ is the amplitude and $\omega$ is the angular frequency.
- Plug in the given values
From the problem, we have:
- Amplitude ( A = 0.5 , \text{m} )
- Angular Frequency ( \omega = 20 , \text{rad/s} )
Substituting the values into the formula: $$ V_{max} = 0.5 \times 20 $$
- Calculate the maximum velocity
Now, calculate the value: $$ V_{max} = 10 , \text{m/s} $$
The maximum velocity is $10 , \text{m/s}$.
More Information
This calculation is based on the relationship of maximum velocity to amplitude and angular frequency in simple harmonic motion. The formula used shows how the peak speed depends directly on these two quantities.
Tips
- Confusing amplitude with displacement: Remember that amplitude refers to the maximum extent of a vibration or oscillation, not the current position.
- Misapplying the formula for maximum velocity; ensure to correctly use the provided values for amplitude and angular frequency.
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