How far does a new corvette go in 8 seconds if its speed steadily increases from 12 m/s to 36 m/s?
Understand the Problem
The question is about calculating the distance traveled by a corvette over 8 seconds while its speed increases steadily from 12 m/s to 36 m/s. This requires applying the formula for distance under uniform acceleration.
Answer
The distance traveled is \( 192\, \text{m} \).
Answer for screen readers
The distance traveled by the corvette is ( 192, \text{m} ).
Steps to Solve
- Identify Initial and Final Speed
The initial speed ( v_i ) is 12 m/s, and the final speed ( v_f ) is 36 m/s.
- Calculate the Average Speed
To find the average speed ( v_{avg} ) when starting from ( v_i ) and increasing to ( v_f ), use the formula:
$$ v_{avg} = \frac{v_i + v_f}{2} $$
Substituting the values:
$$ v_{avg} = \frac{12, \text{m/s} + 36, \text{m/s}}{2} = \frac{48, \text{m/s}}{2} = 24, \text{m/s} $$
- Calculate Distance Traveled
The distance ( d ) traveled can be calculated using the formula:
$$ d = v_{avg} \times t $$
Where ( t ) is the time in seconds. Substituting the average speed and time:
$$ d = 24, \text{m/s} \times 8, \text{s} = 192, \text{m} $$
The distance traveled by the corvette is ( 192, \text{m} ).
More Information
The calculation used average speed due to uniform acceleration, which is a fundamental concept in kinematics. This scenario is applicable in various real-world situations involving steady acceleration.
Tips
- Failing to calculate the average speed correctly by not using the formula ( v_{avg} = \frac{v_i + v_f}{2} ).
- Confusing distance calculations by using just one of the speeds instead of the average.
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