An object accelerates uniformly from rest for 4 seconds. The object's average speed for this time interval is:
Understand the Problem
The question involves the concept of average speed of an object that accelerates uniformly from rest over a time interval, requiring knowledge of physics formulas related to motion.
Answer
The object's average speed for this time interval is \( 2a \).
Answer for screen readers
The object's average speed for this time interval is ( 2a ).
Steps to Solve
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Understanding Average Speed Calculation Average speed is calculated by dividing the total distance traveled by the time taken. For an object accelerating from rest, the formula for distance traveled under uniform acceleration is needed.
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Use the Formula for Distance The formula to calculate the distance traveled by an object under uniform acceleration is: $$ d = \frac{1}{2} a t^2 $$ where ( d ) is the distance, ( a ) is the constant acceleration, and ( t ) is the time.
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Calculate Total Distance for Given Time In this case, substituting ( t = 4 ) seconds into the formula gives: $$ d = \frac{1}{2} a (4)^2 = 8a $$
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Determine Average Speed The average speed ( v_{avg} ) can be calculated by dividing distance ( d ) by time ( t ): $$ v_{avg} = \frac{d}{t} = \frac{8a}{4} = 2a $$
The object's average speed for this time interval is ( 2a ).
More Information
In this case, ( a ) represents the acceleration of the object. The average speed increases linearly with acceleration over the given time interval.
Tips
- Confusing average speed with instantaneous speed: Average speed is total distance divided by total time, whereas instantaneous speed is the speed at a particular point in time.
- Misapplying the distance formula for scenarios with non-uniform acceleration.
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