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### Course: AP®︎/College Calculus AB>Unit 4

Lesson 2: Straight-line motion: connecting position, velocity, and acceleration

# Introduction to one-dimensional motion with calculus

Straight-line motion can be modeled by giving position as a function of time. Calculus helps us learn about velocity, speed, and acceleration, all from our knowledge about the change in position.

## Want to join the conversation?

• : Why acceleration is -6 at t = 0?

At time 0 there is no change in velocity of the object then how can acceleration would have any value ?
• This comes back to the whole definition of derivative as "instantaneous rate of change", which is a little difficult to deal with in physical contexts. The best way to think about it would be perhaps thinking of it as the acceleration being -6 on an infinitesimally short interval around t = 0, instead of at an exact instant.
• Still don't understand the point at the end about velocity. It's a -2 change from 5 to 3 and 3 to 1 so why does it become positive after 1 second
• velocity is dependant on direction, so it can be positive or negative. So if you go in the opposite direction the velocity will be negative
• I don't understand how velocity becomes less negative between the 1st and the 2nd seconds. You're going left from 5 to 3 between 0 and 1 seconds, and then further left from 3 to 1 between 1 and 2 seconds, so how does it become less negative?
• you are slowing down to prepare for a turn, so your velocity will decrease. In this case the velocity was negative in the first place, so it becomes less negative, hence it is slowing down and acceleration is positive
• I am feeling lost after
Can somebody provide alternate explanation ?
• What Sal is saying at is that acceleration is negative when t < 1, zero at t = 1, and positive when t > 1. When acceleration is negative, velocity becomes more negative (which is the same thing as less positive); when acceleration is positive, velocity becomes more positive (less negative).
• does physics graphs always have time in the x axis?
• In physics, time is the independent variable. Thinking of it this way can help "visualize" why things are the way they are dependingly
• is the third derivative the jerk?
• Yes! s'= velocity s''= acceleration s'''=jerk
4th-6th can be called snap, crackle and pop
• Just to make sure, speed is basically the absolute value of the first derivative.
• It isn't the absolute value of any first derivative. Speed is the absolute value of the first derivative of position. For most other physical quantities, the first derivative is called the rate.
• Why velocity is the derivative of time?