in this video we are going to introduce the basics of motion with a focus on distance displacement speed velocity and acceleration definitions of each term and examples will be provided to outline how each is related and to compare similar quantities we'll look at graphically interpreting uniform and non-uniform motion with a focus on how sign and Direction impact our interpretation of motion distance is the length of a path followed between an object's initial and final positions or locations in space this depends on the total amount an object moves not just its starting and ending points displacement on the other hand is the change in the position between an object's initial and final positions its size or magnitude is the length of the shortest linear distance between an object's initial and final positions and its direction is from the initial position to the final position the displacement depends only only on the starting and ending points not on the total amount an object moves for a single movement or Journey an object's distance and displacement may have the same magnitude or the magnitude of the distance the object travels may be greater than the magnitude of its displacement let's consider a scenario in which the ladder is true a car leaves a starting position and travels a winding path to its ending position the distance traveled is the length of the entire path Trav Tred by the car the displacement is the length of the straight line connecting the car's initial and final positions when we report distance we report only a magnitude an object can change direction and the distance it travels is not affected distance is therefore a scalar quantity a quantity that can be meaningfully defined without Direction when we report displacement we report both a magnitude and a direction this direction can be based on a Compass a coordinate within a polar or cartisian system or a simple Direction like forward right or up when the direction in an object is traveling changes its displacement is affected therefore displacement is a vector quantity a quantity that must include direction to be meaningfully defined let's consider how Direction plays a role in distance and displacement in more detail we're going to present a simple Journey a person walking in opposite directions over a period of time we're also going to examine how we can represent this graphically using distance time and position or displacement time graphs let's consider the person walks 2 m east in 1 second then pauses in place for 1 second for this segment of the journey where the person's Direction has not changed the distance traveled 2 m and the displacement 2 m east have the same magnitude the displacement also has a direction e East whereas the distance doesn't next the person turns around and walks 2 m West in 2 seconds then pauses in place for 1 second the person has traveled an additional 2 m bringing their total distance to 4 M however the person has changed Direction and walked back to their starting position their total displacement for the same journey is 0 m as if the person had not left their initial position the person once again turns around and walks 2 m East in 1 second during the 6-second journey the person has traveled a distance of 6 M regardless of which direction they were walking their distance continued to increase during the same 6-second Journey the person has moved 2 m east of their initial position so their displacement is 2 m east when they turned around and walked in the opposite direction their displacement decreased we'll discuss position time graphs and how to interpret them in much more deta detail in another video but for now we can use these graphs to begin considering how we Define and determine an object's speed and velocity during motion speed is the rate of change of position we can express our average speed as the change in distance over the change in time because speed is calculated from a scalar quantity distance speed is also scalar and has only magnitude the average speed of an object in a time interval is the total distance traveled over the total time this is the gradient of a line connecting the initial position to the final position on our distance time graph as shown by this dashed line the speed of any one segment of the journey is the gradient for that segment and may differ from the average speed we can see that during the first second of motion the gradient of the position time graph is steeper than the gradient of the average speed so the object speed in this segment is greater than the average speed however in the the next second the gradient of the position time graph is less steep than the gradient of the average speed so the object speed in this segment is slower than the average speed velocity is also a rate of change but it is the change of position or displacement we can calculate the average velocity as the total change in displacement over the total time we've included arrows on our symbols for velocity and displacement here to denote that these are vector quantities and have both magnitude end direction this notation is commonly used in physics but it is not used by the IB we've included the arrows here to help visually differentiate velocity and displacement from speed and distance moving forward we will differentiate whether the symbol refers to speed or velocity or distance or displacement with context the average velocity of an object over a time interval is the gradient of a line on the position time graph connecting the initial position and the final position shown here by this dashed Line This is the total displacement over the total time the velocity of any one segment of the journey is the gradient for that segment and may differ from the average velocity in the first second of motion the velocity is greater than the average velocity because the gradient of this segment is steeper than the average velocity however in the next second the velocity is slower than the average velocity because the gradient is less steep than the average velocity lastly in the third segment we can see the velocity is negative because the gradient is negative while the average velocity for the entire journey is positive graphically we can clearly see that the magnitude of the average velocity for the journey is lower than the average speed for the same Journey because the gradient of the average velocity line is less steep than the gradient of the average speed line the distance traveled is greater than the displacement for the same period of time if the direction of motion changes during a Time interval the magnitude of the average speed of the object will be greater than the magnitude of the velocity of the object over that time interval because velocity can be positive or negative whereas speed can only be positive so what is the difference between positive and negative velocity an object has positive velocity when its position changes in a positive direction traditionally Positive Directions include North East up right and forward but can be defined in opposite directions it's up to us on a position time graph positive velocity is indicated by a positive gradient an object has negative velocity when its position changes in a negative Direction traditionally negative directions include South West down left and backward once again we can choose which directions to Define as positive and negative for this video we'll stick to the traditional directions being positive and negative on on a position time graph a negative velocity is indicated by a negative gradient thus far we've explored objects that have constant speed or velocity when in motion and that instantaneously change speed or Direction now let's turn to what happens when the velocity of an object changes over time as it's moving this is called acceleration imagine a cyclist moving East a positive direction first slowly at a constant velocity then increasing its velocity over time until they move with a greater constant velocity when the cyclist has a constant velocity their motion on the position time graph is a straight sloping line we can also plot this motion on a velocity time graph where constant velocity is shown as a horizontal line because the cyclist continues to move at the same speed for the whole time interval when the cyclist is accelerating and changing their velocity their motion on a positioned time graph is a curved line curving upward because because the velocity is increasing on the velocity time graph constant acceleration is shown as a straight sloping line just like velocity is the rate of change of position acceleration is the rate of change of velocity the velocity can change when the object changes speed or Direction because acceleration is the rate of change of velocity over time the average acceleration can be calculated as the change in velocity over the time interval the change in velocity can be expanded into V the final velocity minus U the initial velocity this equation rearranges into an equation you may be familiar with from your IB Data Book the final velocity is equal to the initial velocity plus the product of the acceleration and time this equation and other acceleration equations will be covered in a later video for the graph shown we can calculate the acceleration between 2 and 5 Seconds the final velocity is pos4 m/s and the initial velocity is POS 0.25 m/s the cyclist accelerates for 3 seconds the cyclist acceleration is then postive 1.25 m/s squared the average acceleration of an object over a time period can be calculated as the gradient of the Velocity time graph over that time period we explored a cyclist moving in a positive direction while speeding up acceleration being a vector quantity can be positive or negative to add complexity acceleration can be positive while causing an object to either speed up or slow down or negative while causing an object to slow down or speed up how does this work well we must consider the direction of the initial velocity and the direction of the acceleration we'll look at four scenarios involving acceleration first we'll examine an object moving in a positive direction while accelerating in a positive direction both the velocity and acceleration are positive and the object gets faster its speed increases we can see this acceleration on on a position time graph the gradient gets steeper over time we have focused on an object's average velocity thus far but we can also consider an object's instantaneous velocity this is the velocity an object has at a single moment in time we can visually represent the instantaneous velocity as the tangent line to the position time graph at that moment we'll explore instantaneous velocity and tangent lines in more detail in future videos the car's instantaneous velocity increases with time and plotting the instantaneous velocity Against Time produces a linear graph with a positive gradient above the x or time axis next we'll examine an object moving in a negative Direction while accelerating in a negative Direction both the velocity and acceleration are negative and the object gets faster its speed increases we can see this acceleration on a position time graph the gradient again gets steeper over time the same motion on a velocity time graph is a straight line with a negative gradient below the time axis if the object's initial velocity and acceleration are both positive or both negative that is they're in the same direction the object will speed up now let's consider the scenarios in which the initial velocity and acceleration are in opposite directions first let's consider if an object has a positive velocity but accelerates in a negative Direction the object gets slower its speed decreases we can see this acceler ation on a position time graph the gradient gets less steep over time the same motion on a velocity time graph is a straight line with a negative gradient above the time axis the velocity approaches zero as the object slows lastly we'll consider if an object has a negative velocity but accelerates in a positive direction the object again slows down on a position time graph we can see the gradient gets less steep over time on the corresponding velocity time graph the motion is represented by a straight line this time with a positive gradient below the time axis the velocity once again approaches zero as the object slows if the object's initial velocity and acceleration are in opposite directions the object will slow down we mentioned earlier that an object accelerates when its velocity changes and that this can occur if the magnitude of the Velocity or the direction of the velocity changes let's consider a scenario in which the magnitude of the velocity Remains the Same but an object accelerates due to a change in Direction when an object moves with circular motion a concept that will be explored in another video in more detail its instantaneous velocity that is its velocity at any moment in time is always tangent to the circular path the object's change in velocity between any two points on the circle points toward the center of the circle therefore the object accelerates toward the center of the circle despite its speed not changing as as it moves okay so to summarize the key points of this video distance is the length of the path traveled and is a scalar quantity while displacement is the change in position or length of the straight line path from the initial to final position and is a vector quantity an object's distance is greater than its displacement for a journey if the object changes Direction speed and velocity are both rates of change and can be calculated by the gradient of a distance time or position time graph respectively speed is a scalar quantity calculated as the total distance over the total time whereas velocity is a vector quantity calculated as the total displacement over the total time speed can only be positive whereas velocity can be negative if an object is moving in a negative Direction lastly acceleration is the rate of change of velocity and can be calculated by the gradient of a velocity time graph acceleration is a vector quantity and can be positive or negative whether the magnitude of an object's velocity increases decreases or Remains the Same during acceleration is determined by the relative directions of the initial velocity and acceleration