If an object moves with constant acceleration, its velocity must
Understand the Problem
The question is asking what happens to the velocity of an object that is moving with constant acceleration, with multiple choice answers provided for possible outcomes.
Answer
D: change by the same amount each second.
Answer for screen readers
The correct answer is D: change by the same amount each second.
Steps to Solve
- Understand Constant Acceleration
An object with constant acceleration means that its acceleration, $a$, does not change over time. This can be mathematically represented as: $$ a = \frac{\Delta v}{\Delta t} $$ where $\Delta v$ is the change in velocity and $\Delta t$ is the change in time.
- Velocity Change Over Time
Under constant acceleration, the change in velocity ($\Delta v$) is consistent for equal time intervals. This means if we look at velocity after successive time intervals, we can express it as: $$ v(t) = v_0 + at $$ where $v_0$ is the initial velocity.
- Equal Changes in Velocity
If we analyze the formula $v(t) = v_0 + at$, for each second that passes ($\Delta t = 1$), the change in velocity ($\Delta v$) is constant. This leads to the conclusion: $$ \Delta v = a \cdot \Delta t $$ indicating that the velocity changes by a fixed amount every second.
- Identifying Correct Answer
Based on our understanding, the correct interpretation of constant acceleration is that the velocity changes by the same amount each second, which corresponds to option D.
The correct answer is D: change by the same amount each second.
More Information
In physics, constant acceleration implies a uniform change in velocity over time. For example, an object in free fall has a constant acceleration due to gravity, leading to its velocity increasing by approximately 9.81 m/s every second.
Tips
- Confusing constant acceleration with variable acceleration, where velocity may change by varying amounts.
- Misinterpreting acceleration as a direct reflection of velocity itself, rather than a change in velocity over time.
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