To analyze the information provided and relate it to Newton's second law of motion (F = ma), let's examine the results from the trials:
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Trial 1:
- Force applied (F₁) = 10,725 N
- Time to stop (t₁) = 4.00 seconds
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Trial 2:
- Force applied (F₂) = 5,362.5 N
- Time to stop (t₂) = 8.00 seconds
Calculating Acceleration for Each Trial
Using the formula \( a = \frac{F}{m} \):
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For the first trial:
- \( a₁ = \frac{10,725 , \text{N}}{1950 , \text{kg}} \approx 5.49 , \text{m/s}^2 \)
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For the second trial:
- \( a₂ = \frac{5,362.5 , \text{N}}{1950 , \text{kg}} \approx 2.75 , \text{m/s}^2 \)
Understanding the Relationship
From the above calculations:
- The first trial applies a greater force than the second trial, which results in a greater acceleration in the opposite direction (deceleration in this context).
- When the force is doubled (as in moving from second trial to first trial), the acceleration (deceleration) also increases approximately twofold, confirming that the relationship between force and acceleration established by Newton's second law is upheld.
Selecting the Correct Response
Based on the analysis, the correct interpretation is:
Applying double the force to the car will lead to its deceleration at a rate twice as fast.
Conclusion
This option effectively indicates that as force increases, acceleration (or in this case, deceleration) increases proportionally, which is consistent with \( F = ma \).