What is the formula for the speed of a function?

What is the formula for the speed of a function?

• A. v(t)
• B. |v(t)|
• C. v'(t)
• D. ∫ v(t) dt

Answer: (B)

The main idea is that speed is the magnitude of how fast you’re moving, without regard to direction. In one dimension, velocity v(t) can be negative when moving opposite to the positive direction. The instantaneous speed is the absolute value of velocity, |v(t)|, which is always nonnegative. That’s why this option is the best choice: it captures the nonnegative, directionless rate of motion. The other expressions don’t give speed. v(t) is velocity and can be negative. v'(t) is acceleration, the rate of change of velocity. ∫ v(t) dt gives displacement (the total change in position) up to a constant, not speed. For example, if v(t) = -3, the speed is 3.

The main idea is that speed is the magnitude of how fast you’re moving, without regard to direction. In one dimension, velocity v(t) can be negative when moving opposite to the positive direction. The instantaneous speed is the absolute value of velocity, |v(t)|, which is always nonnegative. That’s why this option is the best choice: it captures the nonnegative, directionless rate of motion.

The other expressions don’t give speed. v(t) is velocity and can be negative. v'(t) is acceleration, the rate of change of velocity. ∫ v(t) dt gives displacement (the total change in position) up to a constant, not speed. For example, if v(t) = -3, the speed is 3.