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MonographsHigh SchoolPhysicsRest & Motion | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Created: 24 Feb, 2010; Last Modified: 04 Aug, 2021 The page has been upgraded to a new home. Please follow this link. Rest and Motion – 01Speed & DistanceDistance and Displacement
Distance is defined as the measure of space between two points in units of length, such as the meter. When an object travels from position A to position B (Fig. ), the total length of the path taken to reach B from A is the distance traversed by the object. Distance is usually represented by the variable s. Displacement is the straight-line distance between the starting and ending positions of a body. In Fig. , the length of the straight line connecting the two positions A and B is the displacement. Thus, while distance is a measure of length without regard to direction, displacement measures the change in a body's position in a straight line from the start to the end position. Note that:
To track the position of a body moving in a straight line (displacement), it is convenient to choose a point of origin O on a straight line. Thereafter, all positions on one side of the origin is considered to be positive, while those on the other side are considered negative. Although any side can be chosen to be positive, by convention positions to the right side of origin are considered positive (see Fig. ).
To specify a body's position moving along a straight line, we need to mention its distance from the origin, as well as the direction (positive or negative) relative to the origin. Generally, displacement in one-dimensional (straight-line) motion is represented by x. To indicate the direction, a positive or negative sign is prefixed to the displacement value. Thus a body, whose position is defined as x SpeedSpeed is a measure of how fast a body is moving. It is generally represented by the symbol v. Average SpeedAverage speed of a body during an interval of time is the distance traveled by the body divided by the time interval. If s is the distance covered in time interval t, the average speed vavg is given as .......(1)
Since speed is a ratio of distance over time, its unit is likewise a ratio of the unit of length and the unit of time. In the SI system, where the unit of length is m (meter), and that of time is s (second), the unit of speed becomes m However, in normal usage, speed is normally specified in km As is clear, speed is a derived quantity, "derived" from the fundamental quantities of length and time. Eq. can be rearranged to give equations for:
These need not be committed to memory as long as you remember the original equation Eq.
A bus travels Given, s (i)
(ii)
A car covers Given, s We know that
In real life, a moving object like a car will cover a distance in a given amount of time but at speeds which keep varying during the entire time period. It starts from rest (zero speed), speeds up to continue moving at varying speeds depending upon the road/traffic conditions, and finally slows down to a stop (zero speed) at the destination. Suppose the car covers A body is said to exhibit uniform speed if it moves at a constant speed over an interval of time. This means that the body covers equal distances in each small interval of time within the entire period of motion. A skydiver jumping off a plane from a great height finally reaches a uniform speed (of about
Distance -time graph for uniform speedA distance-time graph plots the distance covered by a moving object against time. The distance is plotted against the y-axis, while the time against the x-axis. Table shows data taken of a bus journey from a bus stand (as the starting point) which begins at 9:00 am and ends at 12:00 noon. The increasing distances of the bus from the bus stand are tabulated against clock time. The journey finally ends at Notice from the table that in each interval of time (of
If the table data is plotted, with the time along the x-axis and distance along the y-axis, we get the distance-time graph as shown in Fig. . The graph is a straight line. Thus, the distance-time graph of a body moving with uniform speed is a straight line. Average speed from distance-time graphThe plot of distance-time graph can be utilised for calculating the speed of the body. Look at the distance-time graph for uniform speed as shown in Fig. . Consider two instants of time, t Thus, during the time interval t
Now, Thus, .......(2)
Note: Do not make the mistake of assuming that a straight line on the distance-time graph denotes that the body travels in a straight line. It may be the case, but straight-line motion and the distance-time graph plot do not relate in this way. If, after plotting the distance-time graph, the value of Now, since the steeper the line, the greater the slope, it implies that steeper lines on the distance-time graph indicate greater speeds. Instantaneous Speed
Instantaneous speed is the speed that a body moves at a particular moment (instant of time). For the earlier bus journey example, where the average speed of the bus for the journey is Since the tabulated data in Table provides data only for a few instants of time and the distances corresponding to them, which happen to be such that the bus covers equal distances in each interval (a very rare possibility in real life), the points plotted on the distance-time graph can be connected by a straight line. However, had the data contained smaller intervals of time, such as the distances for every As illustration, consider the more detailed distance vs. time data points for the same bus journey (with time intervals of
So, as we go into measuring the bus journey in greater detail, the variations in speed become evident. It is when the time intervals get smaller and smaller (5 minutes ... 1 minute … 30 seconds … 1 second …) that the concept of average speed starts translating to the concept of instantaneous speed, where instantaneous speed is mathematically defined as the distance traveled by a body (in a very small interval of time) divided by the time interval. Feedback
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Otherwise, send an email to feedback@mentorials.com with subject line: "Feedback: Speed & Distance". BibliographyHsu, T, Foundations of Physics, 1st edn, MA, USA: CPO Science, 2004. Verma, HC, Foundation Science Physics for Class 9, New Delhi, India: Bharati Bhawan, 2002.
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MonographsHigh SchoolPhysicsRest & Motion | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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