Kinematics Definitions - PhysPrimer

An intro to kinematics, how we characterize motion with motion diagrams and graphs, and the definitions of displacement, velocity, and acceleration.
0:00 Introduction
0:34 Choosing a coordinate system
2:00 Motion Diagrams
4:13 Position vs Time Graph
6:03 Displacement Definition
8:00 Displacement Example 1
9:06 Displacement Example 2
10:27 Velocity Definition
13:38 Instantaneous Velocity
15:41 Velocity Example with Motion Sensor
16:57 Acceleration Definition
18:33 Direction of Acceleration
21:46 Acceleration Example for 2D Motion
23:07 Instantaneous Acceleration
24:39 More Acceleration Examples
25:42 Summary Relating Position, Velocity, and Acceleration
27:36 Try it yourself examples (solutions at end of description)
Opening Image Credit: NASA, ESA, CSA, STScI, Klaus Pontoppidan (STScI), Image Processing: Alyssa Pagan (STScI)
science.nasa.gov/missions/jam...
Solutions to "Try it yourself" examples (and I do recommend trying these yourself BEFORE looking at solution):
1a) Velocity is pointing left (the object is moving from right to left) and the speed is increasing (spacing between dots gets larger), so the acceleration must point in the same direction as the velocity (acceleration points left)
1b) Velocity is still pointing left (the object is moving from right to left) but now the speed is decreasing (spacing between dots gets smaller), so the acceleration points in the opposite direction as velocity (acceleration points right)
1c) For points 1-5, the object is moving upwards (upwards velocity) but the speed is decreasing, so the acceleration points opposite of velocity (acceleration is downwards). For points 5-9, the object is moving downwards (downwards velocity) but now speed is increasing, so acceleration points in the same direction as velocity (acceleration is still downwards). Note that for the entire motion, the acceleration is pointing DOWNWARDS even though the object's velocity is sometimes upwards and sometimes downwards. This motion matches the patterns that we see in projectile motion (if gravity is the only force acting on the object, the acceleration due to gravity will always be downwards).
2) First section, the dog is slowly moving west (x vs t graph has a small, negative slope, and if east is the positive direction, then west is negative). Then the dog moves quickly west (large negative slope). Then the dog stops for a time (slope is zero). Then the dog moves quickly east (large positive slope)

[@KINGSTUNAX]

Love to be the first to comment but again great explanation. One question as I am learning- that is why we do final - initial (is it because change cannot be negative or there is some serious logic behind this because this confuse me alot)

[@PhysicistMichael]

The change in a quantity can definitely be negative if that value is decreasing (the second example I have shows a case for this). Basically this final - initial definition is used so that the change in the quantity will be positive if the value is increasing and negative if the value is decreasing.
For example, let's say at the beginning of the month you have $800 in the bank, and at the end of the month you have $1000 in the bank. The change in those funds are +$200 ($1000 - $800, final - initial), and since the amount of money increased, that change is positive. On the other hand, let's say at the beginning of the month you have $1500 in the bank, and at the end of the month you have $1300, then the change in funds would be -$200 (final - initial, $1300 - $1500). That's what I mean by the change in the quantity will be positive if the value is increasing and negative if the value is decreasing, and similar consistencies hold when considering the change in vector quantities and other applications. That's why this particular definition is more useful.

[@KINGSTUNAX]

@@PhysicistMichael thanks alot for answering this because whenever we talk about change we just subtract the initial value from final like it some kind of formula nobody tend to explain the logic to me ever before. It confused me alot when placing the value while practicing questions and mcqs, Specially incase when the final is -ve value and initial is +ve value_ the overall change is +ve. But the confusion is also caused because of putting wrong sign sometime. Knowing this is very helpful overall in short change can be +ve (increase) or -ve (decrease) and final value - initial value.