Questions: Problem 13: (4% of Assignment Value) A graph of velocity versus time is shown. Which of the following graphs best represents an acceleration curve that is consistent with the above velocity curve? The horizontal axes are scaled identically.

Solution Steps

The given velocity-time graph is a triangle, indicating three distinct phases:

1. Positive constant acceleration (slope is positive) from \( t = 0 \) to \( t = 2 \).
2. Zero acceleration (slope is zero) at the peak from \( t = 2 \) to \( t = 4 \).
3. Negative constant acceleration (slope is negative) from \( t = 4 \) to \( t = 6 \).

Acceleration is the derivative of velocity with respect to time. Therefore:

1. From \( t = 0 \) to \( t = 2 \), the acceleration is positive and constant.
2. From \( t = 2 \) to \( t = 4 \), the acceleration is zero.
3. From \( t = 4 \) to \( t = 6 \), the acceleration is negative and constant.

We need to find the graph that shows:

1. A positive constant value from \( t = 0 \) to \( t = 2 \).
2. A zero value from \( t = 2 \) to \( t = 4 \).
3. A negative constant value from \( t = 4 \) to \( t = 6 \).

Final Answer