Thus usually starts with one-dimensional motion and moves on to motion in two dimensions up-down and side-to-side such as projectile motion, introducing Earth's unique gravitational acceleration of 9. Distance and displacement are commonly confused terms in physics that are important to get correct.
The difference between a vector quantity and a scalar quantity is that vector quantities include information about direction; scalar quantities are simply numbers. Anything that moves in relation to a fixed reference frame is covering distance. How is this possible? Both distance and speed are scalar quantities, so they are naturally found together. Because displacement is a vector quantity, it, not distance, must be used to find average velocity, another vector quantity.
All you'd have to do is make sure you pulled over in the same spot the officer first spotted you, and you could argue that, the distance of your trip aside, your displacement is clearly zero, rendering your velocity zero by definition. Okay, maybe not such a good idea for various reasons! The negative sign is important because a frame of reference was chosen to situate the park in the positive direction on the x-axis.
Eyewitnesses could feel the intense heat from the fireball, and the blast wave from the explosion blew out windows in buildings. The blast wave took approximately 2 minutes 30 seconds to reach ground level. Skip to content 3 Motion Along a Straight Line.
Learning Objectives By the end of this section, you will be able to: Define position, displacement, and distance traveled. Calculate the total displacement given the position as a function of time.
Determine the total distance traveled. Calculate the average velocity given the displacement and elapsed time. Position To describe the motion of an object, you must first be able to describe its position x : where it is at any particular time.
Figure 3. Their motion can be described by their change in position, or displacement, in a frame of reference. If right is positive and an object moves 2 m to the right, then 4 m to the left, the individual displacements are 2 m and m, respectively. Her position relative to Earth is given by x. Average Velocity To calculate the other physical quantities in kinematics we must introduce the time variable.
For each position , we assign a particular time. Average Velocity. Example Delivering Flyers Jill sets out from her home to deliver flyers for her yard sale, traveling due east along her street lined with houses. At km and 9 minutes later she runs out of flyers and has to retrace her steps back to her house to get more. This third leg of her trip takes minutes.
At this point she turns back toward her house, heading west. After km and minutes she stops to rest. What is the magnitude of the final displacement?
What is the average velocity during her entire trip? What is the total distance traveled? Make a graph of position versus time. The average velocity is the slope of a line connecting the initial and final points. Check Your Understanding A cyclist rides 3 km west and then turns around and rides 2 km east. Summary Kinematics is the description of motion without considering its causes. In this chapter, it is limited to motion along a straight line, called one-dimensional motion.
Displacement is the change in position of an object. The SI unit for displacement is the meter. Displacement has direction as well as magnitude. Distance traveled is the total length of the path traveled between two positions. Time is measured in terms of change. The time between two position points and is. Elapsed time for an event is , where is the final time and is the initial time. Average velocity is defined as displacement divided by elapsed time.
If and are two position time points, the average velocity between these points is. A cyclist rides 3 km west and then turns around and rides 2 km east. The displacement is negative because we take east to be positive and west to be negative.
The SI unit for displacement is the meter m. Displacement has a direction as well as a magnitude. Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Specifically identify each quantity in your example. Under what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and displacement are exactly the same?
Bacteria move back and forth by using their flagella structures that look like little tails. The total distance traveled by a bacterium is large for its size, while its displacement is small. Why is this? Find the following for path A in Figure 5: a The distance traveled. Find the following for path D in Figure 5: a The distance traveled.
Skip to main content. Search for:. Displacement Learning Objectives By the end of this section, you will be able to: Define position, displacement, distance, and distance traveled. Explain the relationship between position and displacement. Distinguish between displacement and distance traveled. Calculate displacement and distance given initial position, final position, and the path between the two. Misconception Alert: Distance Traveled vs. Magnitude of Displacement It is important to note that the distance traveled , however, can be greater than the magnitude of the displacement by magnitude, we mean just the size of the displacement without regard to its direction; that is, just a number with a unit.
Check Your Understanding A cyclist rides 3 km west and then turns around and rides 2 km east. Figure 4.
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