https://file.aiquickdraw.com/mathbot/file/1729834418330jg336swh.jpg

I see the image you've uploaded is related to a problem involving the motion of a particle, focusing on its position, velocity, and acceleration over time. It includes steps such as calculating velocity, acceleration, and interpreting graphical data.

Let me help clarify the key parts or solve specific portions of it:

1. It looks like part (h) asks when the particle is speeding up or slowing down, requiring you to use interval notation. This generally depends on the signs of both velocity \( v(t) \) and acceleration \( a(t) \). The particle speeds up when \( v(t) \) and \( a(t) \) have the same sign (both positive or both negative), and slows down when they have opposite signs.

Would you like me to focus on this part, or do you want a detailed explanation of any specific section from the problem?

A particle moves according to a law of motion s = f(t), where t is measured in seconds and s in feet. The problem involves calculating the velocity, acceleration, and interpreting when the particle is speeding up or slowing down, using interval notation.

This problem focuses on analyzing a particle's motion through its velocity and acceleration functions. Learn to calculate these rates of change and determine when the particle is speeding up or slowing down using calculus. Suitable for advanced high school or college-level students.

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