An object accelerates uniformly from rest for 4 seconds. The object's average speed for this time interval is: a) (1/2)at b) (1/2)at^2 c) (3/2)at d) 2at
Understand the Problem
The question is asking for the average speed of an object that accelerates uniformly from rest over a time interval of 4 seconds. This involves using the physics formula for average speed under uniform acceleration.
Answer
The average speed is $v_{\text{avg}} = \frac{1}{2}at$.
Answer for screen readers
The object's average speed for this time interval is $v_{\text{avg}} = \frac{1}{2}at$.
Steps to Solve
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Identify Given Information The object accelerates uniformly from rest, so the initial velocity $u = 0$. The time interval is $t = 4$ seconds.
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Use the Formula for Average Speed The formula for average speed ($v_{\text{avg}}$) under uniform acceleration is given by: $$ v_{\text{avg}} = \frac{u + v}{2} $$ where $u$ is the initial velocity and $v$ is the final velocity.
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Determine Final Velocity The final velocity ($v$) can be calculated using the formula: $$ v = u + at $$ Substituting $u = 0$: $$ v = 0 + at = at $$
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Calculate Average Speed Substituting $u$ and $v$ into the average speed formula: $$ v_{\text{avg}} = \frac{0 + at}{2} $$
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Final Expression for Average Speed Thus, the average speed is: $$ v_{\text{avg}} = \frac{1}{2}at $$
The object's average speed for this time interval is $v_{\text{avg}} = \frac{1}{2}at$.
More Information
The average speed during uniform acceleration from rest is always half of the product of acceleration and time. This concept is essential in physics and is frequently applied in problems involving linear motion.
Tips
- Misapplying the formula for average speed by forgetting to account for the initial speed being zero.
- Confusing average speed with total distance traveled or final velocity.
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